Welcome to the web page of Extracta Mathematicae. We have tried our best, but in case any user detects any inaccuracy or malfunction, please contact us here and we will solve it as soon as possible. Extracta Mathematicae (E.M.) publishes quality research papers that contain innovative contributions in the areas covered by the members of the Editorial Board. E.M. is also open to consider well written survey papers. Publishing in E.M. is exempt from fees of any kind, and all documents are freely available for reading. E.M. publishes two issues a year under a Creative Commons License Attribution-Non Commercial 4.0 Unported license. The online version is free and open access. E.M. uses a standard blind peer review process, following the COPE Code of Conduct. E.M. is edited and published in Badajoz (Spain) by the Instituto de Matemáticas de la Universidad de Extremadura (IMUEX), under the auspices of this university and the cooperation of the Departamento de Matemáticas and the Servicio de Publicaciones. We are uploading the previous issues here. In the meanwhile, all volumes, published uninterruptedly since 1986, are available online at: UNEx-Extracta or Dialnet E.M. has been recently evaluated and accepted for inclusion in Scopus (Scopus Sources List, Accepted titles). These are the latest volumes of E.M. in Scopus. E.M. is abstracted and indexed in Mathematical Reviews and Zentralblatt MATH. The AMS-Mathematical Citation Quotient (MCQ) average (2000-2017) for E.M. is 0.25 (all publications MCQ average 2000-2017 is 0.22) and the 2024-MCQ is 0.25 (2024-MCQ all journal median is 0.21). The printed version is exchanged with 117 journals in 36 countries all over the world. E.M. is indexed in DOAJ, the Directory of Open Access Journals, as well as in Latindex 2.0, and is a member of Free Journal Network. E.M. has obtained the Fecyt Quality seal 2021 and it was renewed in 2022, 2023 and 2024. E.M. uses Open Journal System OJS. 2024 data: From 1st January to 31th December 2024, 104 manuscripts have been received in E.M., and 12 papers have been accepted for publication. Regular number of reviewers for each manuscript: 2. Speed (average): Submission to first decision (all received manuscripts): 36 days Submission to definitive decision (all received manuscripts): 46 days Submission to first decision (accepted manuscripts): 100 days Submission to definitive decision (accepted manuscripts): 134 days Acceptance to online publication: 47 days Acceptance to print publication: 121 days.
Servicio de Publicaciones, Universidad de Extremadura
On a cohomological characterization of free profinite products of three profinite groups with amalgamated subgroups
Let C be the class of all finite solvable groups and n ≥ 2 be an integer. In this paper, we present constructions of free pro-C products of n pro-C groups with amalgamated subgroups, and of free pro-C products of n pro-C groups with commuting subgroups. We also provide conditions under which a given free pro-C product of three pro-C groups with amalgamated subgroups can be written as a free pro-C product with amalgamated subgroup of two free pro-C products with amalgamated subgroups. Furthermore, we characterize –using cohomological conditions– when a pro-C group is the free pro-C product of three of its subgroups with amalgamated subgroups. Finally, we obtain a similar characterization for free pro-C products of two pro-C groups with commuting subgroups.
free pro-C product of pro-C groups with amalgamation
free pro-C product of pro-C groups with commuting subgroups
Copyright (c) 2026 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
Two miniatures relating the 2 × 2 minors of a square matrix and the symmetric group
In the first miniature we recall a puzzle proposed by Martin Gardner in 1957 and refreshed by Blasco in 2014. We prove some properties of the matrices involved. We show that Gardner magical matrices are tropically singular. In the second miniature we construct a counterexample to the following conjecture by R. Flores: for a square matrix A = (aij ) of size n, if for each permutation σ there exists a 2 × 2 minor of A such that aσ(k)k aσ(l)l - aσ(k)l aσ(l)k vanishes, then determinant of A vanishes.
Copyright (c) 2026 The author https://creativecommons.org/licenses/by-nc-sa/4.0
Tangent structures for divided power algebras
We build a tangent structure on the category of divided power algebras using a particular notion of semidirect product. We show that this tangent structure admits an adjoint tangent structure, which involves a version of Khäler differentials, and which is similar to the Zariski cotangent space for affine schemes. We study vector fields and differential bundles for these two structures, which correspond respectively to a notion of special derivation, and to the category of modules over the underlying commutative algebra of a given divided power algebra.
Binet’s formula for operator-valued recursive sequences and the operator moment problem
We derive a Binet-type formula for operator-valued sequences satisfying linear recurrence relations, extending the classical scalar case to the setting of bounded operators on Hilbert spaces. In this framework, we analyze the operator moment problem as an application, establishing new connections between recursive operator sequences and moment sequences.
Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc-sa/4.0
In this paper we study the (co)homology of Tanabe algebras, which are a family of subalgebras of the partition algebras exhibiting a Schur–Weyl duality with certain complex reflection groups. The homology of the partition algebras has been shown to be related to the homology of the symmetric groups by Boyd–Hepworth–Patzt and the results they obtain depend on a parameter. In all known results, the homology of a diagram algebra is dependent on one of two things: the invertibility of a parameter in the ground ring or the parity of the positive integer indexing the number of pairs of vertices. We show that the (co)homology of Tanabe algebras is isomorphic to the (co)homology of the symmetric groups and that this is independent of both the parameter and the parity of the index. To the best of our knowledge, this is the first example of a result of this sort. Along the way we will also study the (co)homology of uniform block permutation algebras and totally propagating partition algebras as well collecting cohomological analogues of known results for the homology of partition algebras and Jones annular algebras.
Metrizability of the strong dual: equivalent topological characterizations
This short article presents several equivalent topological characterizations for the metrizability of the strong dual of a locally convex Hausdorff space. Among our key findings, we establish that the metrizability of the strong dual is precisely equivalent to it being a q-space.
Copyright (c) 2025 Subiman Kundu, Varun Jindal https://creativecommons.org/licenses/by-nc-sa/4.0
The polynomial cluster value problem for Banach spaces
We reduce the polynomial cluster value problem for the algebra of bounded analytic functions, H ∞ , on the ball of Banach spaces X to the same polynomial cluster value problem for H ∞ but on the ball of those spaces which are `1 -sums of finite dimensional spaces.
Four-dimensional quasi-Einstein non-reductive homogeneous spaces are Einstein
We investigate quasi-Einstein structures on four-dimensional non-reductive homogeneous spaces. We show that contrary to the Ricci solitons structures, quasi-Einstein structures display a strong rigidity in the sense that every such a structure is necessarily Einstein.
Algebraic realization of chain maps in differential graded algebras over a principal ideal domain
Let R be a principal ideal domain, and let (T (V ), ∂) and (T (W ), δ) be two free differential graded R-algebras. Let (V, d) and (W, d0 ) denote the chain complexes of the indecomposables of (T (V ), ∂) and (T (W ), δ), respectively. Given a chain map ξ* : (V, d) → (W, d'), this paper addresses the problem of determining whether there exists a DGA-map α : (T (V ), ∂) → (T (W ), δ) such that H* (α) = H* (ξ* ).
Copyright (c) 2025 The author https://creativecommons.org/licenses/by-nc-sa/4.0
Fourth Hankel and Toeplitz determinant estimates for certain analytic functions associated with Four Leaf function
The objective of this paper is to establish initial coefficient inequalities, Upper bounds to the Hankel and Toeplitz determinants for certain normalized univalent functions defined on the open unit disk D in the complex plane related to the analytic function ϕ4L (z) = 1 + 5z/6 + z5/6 that maps the open unit disk in the complex plane onto the interior of four leaf shaped domain in the right half of the complex plane.
We provide infinite-dimensional versions of analytic gap dichotomies, in the sense that a sequence of analytic hereditary families {Ip }p<ω of subsets of a countable set Ω is either countably separated or there is a tree structure inside Ω in which p-chains are sets from Ip . A topological version of this is that if K is a separable Rosenthal compact space, then either K is a continuous image of a finite-to-one preimage of a metric compactum or there is a tree structure inside K in which p-chains inside every branch form a relatively discrete family of sets.
Copyright (c) 2025 The authors https://creativecommons.org/licenses/by-nc/4.0/
On lifts of linear tensor fields to Weil bundles
In this paper, we generalize for an arbitrary double vector bundle, some results on linear tensor fields. Moreover we study some properties of their lifts with respect to a product preserving bundle functor.
Spectrally distinguishing symmetric spaces II
The action of the subgroup G2 of SO(7) (resp. Spin(7) of SO(8)) on the Grassmannian space M = SO(7)/(SO(5)×SO(2)) (resp. M = SO(8)/(SO(5)×SO(3)) ) is still transitive. We prove that the spectrum (i.e. the collection of eigenvalues of its Laplace-Beltrami operator) of a symmetric metric g0 on M coincides with the spectrum of a G2-invariant (resp. Spin(7)-invariant) metric g on M only if g0 and g are isometric. As a consequence, each non-flat compact irreducible symmetric space of non-group type is spectrally unique among the family of all currently known homogeneous metrics on its underlying differentiable manifold.
On the coordinates of minimal vectors in a Minkowski-reduced basis
Finding the shortest non-zero vectors in a lattice is a computationally hard problem (NP-hard in general dimensions), making results in low dimensions particularly important in lattice reduction theory. This paper focuses on the coordinates of minimal lattice vectors when expressed in a Minkowski-reduced basis. By applying Ryskov’s findings on admissible centerings and Tammela’s work characterizing Minkowski-reduced forms via a finite set of inequalities (up to dimension 6), we demonstrate sharp bounds on the absolute values of these coordinates. Specifically, we show that for dimensions n ≤ 6, the absolute values of the coordinates of any minimal vector with respect to a Minkowski-reduced basis are bounded by 1 (for n = 2, 3), 2 (for n = 4, 5), and 3 (for n = 6). This refines bounds implicitly available from Tammela’s results by combining geometric arguments from lattice theory, admissible centering theory, and reduction theory.
Copyright (c) 2025 The author https://creativecommons.org/licenses/by-nc/4.0/
Isocanted cube: the lower Lebesgue volumes, incidence numbers and symmetries of this d–dimensional tile
Let d ≥ 2. In this paper we prove that Id(ℓ, a) fills Rd face–to–face by translations. We prove that the symmetry group of Id(ℓ, a) contains the product of cyclic groups Cd × C2 as a subgroup. We compute the Lebesgue j–volume (i.e., the sum of the Lebesgue j–measures of the j–faces) of Id(ℓ, a), for 1 ≤ j < d. We compute the incidence numbers (as defined by Grünbaum) of the faces of Id(ℓ, a).
The easiest polynomial differential systems in R^3 having an invariant cylinder
This paper answers the following two questions: What are the easiest polynomial differential systems in R3 having an invariant hyperbolic, parabolic or elliptic cylinder?, and for such polynomial differential systems what are their phase portraits on such invariant cylinders?
A study on W9-curvature tensor within the framework of Lorentzian para-Sasakian manifold
This article focuses on the study of Lorentzian para-Sasakian manifolds Mn . It demonstrates that a W9-semisymmetric Lorentzian para-Sasakian manifold is a W9-flat manifold. Additionally, we explore Lorentzian para-Sasakian manifolds that satisfy the ζ-W9-flat condition, revealing that they represent a special type of η-Einstein manifold. Furthermore, it is shown that a W9-flat Lorentzian para-Sasakian manifold is a flat manifold. We also investigate Lorentzian para-Sasakian manifolds that meet W9-recurrent and ϕ-W9-semisymmetric conditions, presenting several significant results from this analysis. At last, we explore η-Ricci Solitons on Lorentzian para-Sasakian manifold satisfying W9(ζ, F1 ) · S = 0.
Accessible operators on ultraproducts of Banach spaces
We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps. We provide a bridge between these “accessible” operators and the theory of twisted sums through the so-called quasilinear maps. Thus, for many pairs of Banach spaces X and Y , there is an “accessible” operator XU → YU that is not the ultraproduct of a family of operators X → Y if and only if there is a short exact sequence of quasi-Banach spaces and operators 0 → Y → Z → X → 0 that does not split. We then adapt classical work by Ribe and Kalton–Peck to exhibit pretty concrete examples of accessible functionals and endomorphisms for the sequence spaces lp The paper is organized so that the main ideas are accessible to readers working on ultraproducts and requires only a rustic knowledge of Banach space theory.
This is a survey of known results and still open problems on characteristic properties of classes of homothetic convex sets in the n-dimensional Euclidean space. These properties are formulated in terms of orthogonal projections, plane sections, homothety classes, Choquet simplices, and homothetic tilings and partitions.
Copyright (c) 2024 The author https://creativecommons.org/licenses/by-nc/4.0/
In this article we study the n-homogeneous polynomials P that are c-continuous on bounded subsets of l1 . We show that P can be decomposed in the form R + Q, where Q and R are n-homogeneous polynomials, with R weakly star continuous and Q (x) = 0 for all x ∈ ker u for u = (1, 1, . . . , 1, . . . ). We conclude that P = Σ un−j ⊗ Rj , where R is a weakly star continuous j-homogeneous polynomial for j = 0, 1, . . . , n.
Some operators on finite-dimensional non-Archimedean normed spaces
In this paper, we are interested in the study of certain operators in non-Archimedean normed spaces of finite dimension. We introduce the notion of p-delta function, then we characterize the simple operators, the similarities and the expansions. We show if E has an orthogonal basis, then each injective operator on E is the composition of an isometry and an expansion.
Some applications of Q-points and Lebesgue filters to Banach spaces
We present a new characterization of Q-point ultrafilters and use it to optimize the result of Avilés, Martı́nez-Cervantes, and Rueda Zoca linking the existence of L-orthogonal sequences and L-orthogonal elements in Banach spaces via ultrafilter limits.
Copyright (c) 2024 The authors https://creativecommons.org/licenses/by-nc/4.0/
A spectral theorem for a non-Archimedean valued field whose residue field is formally real
In this paper, we will prove a spectral theorem for self-adjoint compactoid operators. Also, we will study the condition on which the coefficient field must be imposed. In order to get the theorems, we will use the Fredholm theory for compactoid operators. Moreover, the property of maximal complete field is important for our study. These facts will allow us to find that the spectral theorem depends only on the residue class field, and is independent of the valuation group of the coefficient field. As a result, we can settle the problem of the spectral theorem in the case where the residue class field is formally real.
The Arens-Calderon theorem for commutative topological algebras
A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a0 , . . . , an∈ A with a0 ∈ Rad(A) and a1 an invertible element of k A, then there exists y ∈ Rad(A) such that Σ ak yk = 0. In this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra CX into a commutative Banach algebra.
⊗-Pure model structure on the category of N -complexes
Let G be a closed symmetric monoidal concrete Grothendieck category. In this paper, we introduce a model structure on (CN (G), P⊗dw ) the exact category of N -complexes with the degree-wise ⊗-pure exact structure. Our result is based on the Gillespie’s Theorem by introducing two compatible cotorsion pairs on this category.
On lifts of symplectic vector bundles and connections to Weil bundles
In this paper, we generalize to Frobenius-Weil bundles some lifts of symplectic manifolds and symplectic vector bundles.
Unbounded generalized B-Fredholm operators
In this paper, we investigate a new class of unbounded linear operators, that is, the unbounded generalized B-Fredholm operators in Banach space. More explicitly, we provide a characterization of this class of operators and some of its basic properties on a Banach space. Moreover, we study the generalized B-Fredholm spectrum and we prove a perturbation result of an unbounded generalized B-Fredholm operator under a commuting power finite-rank operator.
A topological characterization of an almost Boolean algebra
For any Boolean space X and a discrete almost distributive lattice D, it is proved that the set C(X, D) of all continuous mappings of X into D, when D is equipped with the discrete topology, is an almost Boolean algebra under pointwise operations. Conversely, it is proved that any almost Boolean algebra is a homomorphic image of C(X,D) for a suitable Boolean space X and a discrete almost distributive lattice D.
The current state of play in the Landsberg-Berwald problem of Finsler geometry
A progress report on the (still unresolved) Landsberg-Berwald problem of Finsler geometry: whether there can be non-Berwaldian regular Landsberg spaces.
Copyright (c) 2024 The author https://creativecommons.org/licenses/by-nc/3.0/
On discontinuity of derivations, inducing inequivalent complete metric topologies
We give an elementary method for constructing commutative Fréchet algebras with non-unique Fréchet algebra topology. The result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined among other useful applications. We give an affirmative answer to a question of Loy (1974) for Fréchet algebras. We also obtain the uniqueness of the Fréchet algebra topology of certain Fréchet algebras with finite dimensional radicals.
Fréchet algebra of power series in infinitely many indeterminates
(in)equivalent Fréchet algebra topologies