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Mathematics
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Advanced Research in Pure and Applied Algebra, 2nd Edition
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Advanced Research in Pure and Applied Algebra, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "A: Algebra and Logic".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 3124

Special Issue Editor

Prof. Dr. Xiaomin Tang

E-Mail Website
Guest Editor
School of Mathematical Science, Heilongjiang University, Harbin 150080, China
Interests: lie theory; cluster algebra; brace
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are delighted to announce the call for papers for the 2nd Edition of the Special Issue “Advanced Research in Pure and Applied Algebra” within the Journal Mathematics, Section A: Algebra and Logic. As the Guest Editor of this Special Issue, I aim to assemble a collection of high-impact research that showcases the latest advancements, innovative methodologies, and critical insights across diverse subfields of pure and applied algebra. This platform is designed to foster academic dialogue, facilitate knowledge dissemination, and strengthen collaborative networks among researchers globally.

This Special Issue welcomes original research papers, comprehensive review articles, and novel perspectives focusing on a broad spectrum of algebraic topics. Key thematic areas include, but are not limited to, Lie algebra and Lie superalgebra, associative algebra, representation theory, cluster algebra, Rota-Baxter algebra, group theory, braces, quantum algebra, and matrix algebra. We particularly encourage submissions that address unresolved questions, propose innovative frameworks, or explore cross-disciplinary applications of algebraic theories, thereby pushing the boundaries of current research in the field.

With decades of experience in algebraic research, my work centers on Lie theory and its applications—encompassing the structure and representation of Lie (super)algebras, quantum groups, and cluster algebras. Having led and participated in over 10 national and provincial-level research projects, published more than 50 SCI-indexed papers, and authored/co-authored 2 monographs and textbooks, I bring a wealth of expertise to oversee the editorial process. Together with the editorial team, I am committed to conducting a rigorous, fair, and timely peer review to ensure that this Special Issue maintains the highest academic standards.

The deadline for manuscript submissions is 31 May 2026. We sincerely invite researchers, scholars, and practitioners from academia and industry to contribute their impactful work. For submission guidelines, editorial policies, and further details, please visit the journal’s official website or contact me directly via the provided email address. We look forward to your valuable contributions and to shaping a landmark special issue that advances the frontiers of pure and applied algebra.

Prof. Dr. Xiaomin Tang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • lie Algebra and lie superalgebra
  • associative algebra
  • eepresentation theory
  • cluster algebra
  • Rota-Baxter algebra
  • group theory
  • braces
  • quantum algebra
  • matrix algebra

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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71 pages, 727 KB  
Article
Notes on Number Theory
by Miroslav Stoenchev, Slavi Georgiev and Venelin Todorov
Mathematics 2026, 14(4), 697; https://doi.org/10.3390/math14040697 - 16 Feb 2026
Viewed by 972
Abstract
This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-dimensional Q-algebras (via [...] Read more.
This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-dimensional Q-algebras (via multiplication operators and matrix representations), leading naturally to the arithmetic invariants—trace, norm, and discriminant—and to the ring of integers, ideals, Dedekind domains, and the ideal class group. We then develop the classical theory of cyclotomic fields, emphasizing their Galois structure and their role in abelian extensions of Q. Next, we discuss ramification in general extensions, including decomposition and inertia groups, the Frobenius element, and the Chebotarev density theorem. The exposition continues with a concise algebraic introduction to elliptic curves and their L-functions, and it places key conjectural links (including Birch and Swinnerton-Dyer) in context. Finally, a collection of examples highlights a common operational language between fractional calculus and number theory: Laplace and Mellin transforms turn convolution-type operators into multiplication, clarifying the appearance of Γ-factors, Dirichlet series, and zeta- and L-function structures in both settings. Full article
(This article belongs to the Special Issue Advanced Research in Pure and Applied Algebra, 2nd Edition)
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11 pages, 275 KB  
Article
On Axis-Reversible Rings
by Muhammad Saad and Majed Zailaee
Mathematics 2026, 14(3), 492; https://doi.org/10.3390/math14030492 - 30 Jan 2026
Viewed by 442
Abstract
This work explores the notion of axis-reversible rings, a generalization of axis-commutative rings. The objective is to investigate their characteristics and relevance within the wider context of ring theory. This paper defines axis-reversibility and demonstrates its importance through many examples. It also analyzes [...] Read more.
This work explores the notion of axis-reversible rings, a generalization of axis-commutative rings. The objective is to investigate their characteristics and relevance within the wider context of ring theory. This paper defines axis-reversibility and demonstrates its importance through many examples. It also analyzes the characteristics of several matrix rings, elucidating the conditions under which a ring can be deemed axis-reversible. This paper examines the relationship between axis-reversibility and other significant ring qualities, such as reducedness and semiprimeness, through comprehensive arguments and proofs. This study provides novel perspectives on non-commutative rings, enhancing our comprehension of algebraic structures. Full article
(This article belongs to the Special Issue Advanced Research in Pure and Applied Algebra, 2nd Edition)
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12 pages, 259 KB  
Article
Generalized Derivations in Rings and Their Applications to Banach Algebra
by Amal S. Alali, Emine Koç Sögütcü, Zeliha Bedir and Nadeem ur Rehman
Mathematics 2026, 14(2), 295; https://doi.org/10.3390/math14020295 - 13 Jan 2026
Viewed by 722
Abstract
Let R be a prime ring, and let F denote a generalized derivation associated with a derivation d of R. Consider I as a nonzero ideal of R, and let m,n,k,l be fixed positive integers. [...] Read more.
Let R be a prime ring, and let F denote a generalized derivation associated with a derivation d of R. Consider I as a nonzero ideal of R, and let m,n,k,l be fixed positive integers. In this study, we explore the behavior of the generalized derivation F within the structures of both prime and semiprime rings that satisfy the functional identity [F(η),d(τ)]m=ηn[η,τ]lηk, ∀,η,τ∈I. Furthermore, we extend this investigation to the framework of Banach algebras, analyzing how generalized derivations operate in such algebras. A comparative discussion is also presented to highlight the distinctions and similarities in the behavior of generalized derivations within Banach algebraic settings under the above structural condition. Full article
(This article belongs to the Special Issue Advanced Research in Pure and Applied Algebra, 2nd Edition)
14 pages, 290 KB  
Article
Nagata and Serre Conjecture Rings: A Unified Pullback Perspective
by Noômen Jarboui and Bana Al Subaiei
Mathematics 2026, 14(2), 237; https://doi.org/10.3390/math14020237 - 8 Jan 2026
Viewed by 547
Abstract
We study the strong S-property for Nagata and Serre conjecture rings through the framework of (T,M,D) construction rings, providing a unified approach that streamlines and extends previous results. Our main contribution is a concise, conceptual proof [...] Read more.
We study the strong S-property for Nagata and Serre conjecture rings through the framework of (T,M,D) construction rings, providing a unified approach that streamlines and extends previous results. Our main contribution is a concise, conceptual proof showing that the strong S-property of R(X) versus R⟨X⟩ depends solely on the transcendence degree of the residue field extension K/k, where k is the quotient field of D. This perspective yields new, transparent counterexamples to both the Malik–Mott conjecture and a question of Cahen et al., and provides a clear characterization of the catenarity of Serre conjecture rings, R⟨n⟩. The approach is based on pullback constructions and the geometric structure of prime ideals, replacing intricate case analyses with arguments driven by natural invariants. Full article
(This article belongs to the Special Issue Advanced Research in Pure and Applied Algebra, 2nd Edition)
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