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Axioms
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Advances in Applied Algebra and Related Topics
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Advances in Applied Algebra and Related Topics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Algebra and Number Theory".

Deadline for manuscript submissions: closed (30 April 2026) | Viewed by 6960

Special Issue Editors

Dr. Filipa Soares de Almeida

E-Mail Website
Guest Editor
Departmento de Matemática, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisbon, Portugal
Interests: Algebra; applied algebra; mathematical modelling
Dr. Fabio Caldarola

E-Mail
Guest Editor
Department of Mathematics and Computer Science, Cubo 31/A, Università della Calabria, 87036 Rende, Italy
Interests: number theory; iwasawa theory; combinatorics; fibonacci numbers; mumber sequences; graph theory; unimaginable numbers; combinatorics on words; fractal geometry; polytopes; elliptic curves; cryptography; applied mathematics; cellular automata; mathematical models; chaos theory; nonlinear dynamics; shallow water
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In this Special Issue, we focus on cutting-edge algebra applications at the crossroads of theory and application. This collection delves into the dynamic landscape where algebraic principles are powerful tools to unravel real-world challenges across diverse domains. From cryptography and computer science to data analysis and engineering applications, this Special Issue aims to spotlight the transformative impact of applied algebra.

The primary goal is to showcase recent advancements that bridge the theoretical elegance of algebraic structures with their practical utility, emphasizing their pivotal role in addressing contemporary problems. We invite contributions that demonstrate the versatility and applicability of algebraic concepts, including but not limited to linear algebra, group theory, ring theory, number theory, and polynomial algebra. The scope extends to applications in cryptography, data science, mathematical modeling, optimization problems, and beyond.

Contributors are encouraged to expose how algebraic methodologies provide innovative solutions in areas such as coding theory, computational algebra, and algebraic geometry. By bringing together researchers and practitioners, we aim to foster a rich exchange of ideas, providing a deeper understanding of how algebraic approaches contribute to the ever-evolving landscape of applied sciences. "Advances in Applied Algebra and Related Topics" aims to contribute to shaping the future of applied algebra and its profound impact on technological advancements and problem-solving methodologies.

Dr. Filipa Soares de Almeida
Prof. Dr. Fabio Caldarola
Guest Editors

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. Axioms is an international peer-reviewed open access monthly 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 2400 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

  • applied algebra
  • coding theory
  • computer science
  • cryptography
  • data analysis
  • mathematical modeling
  • number theory
  • optimization problems

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Published Papers (6 papers)

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Research

12 pages, 259 KB  
Article
From Dedekind’s Level 12 Identities to Combinatorial Structures of Colored Partitions
by Fatemah Mofarreh, Arooj Fatima and Ahmer Ali
Axioms 2026, 15(4), 270; https://doi.org/10.3390/axioms15040270 - 8 Apr 2026
Cited by 1 | Viewed by 363
Abstract
The Dedekind η-function plays an important role in number theory, particularly in the study of modular forms, q-series, and partition identities. In this paper, we investigate several level-12 η-function identities and examine their combinatorial implications. These identities are obtained from [...] Read more.
The Dedekind η-function plays an important role in number theory, particularly in the study of modular forms, q-series, and partition identities. In this paper, we investigate several level-12 η-function identities and examine their combinatorial implications. These identities are obtained from algebraic transformations of known expansions involving mock theta functions, which were originally introduced by Srinivasa Ramanujan. By employing classical q-series techniques and modular transformations, we derive identities that reveal interesting relationships among η-functions. We further interpret these identities combinatorially to establish correspondences between specific classes of colored partitions with prescribed color restrictions. These results provide new insights into the structure of colored partition functions and highlight the interplay between mock theta functions, Dedekind η-function identities, and combinatorial partition theory. Our findings contribute to a deeper understanding of the connections between modular forms and colored partitions and suggest further directions for research in number theory and combinatorics. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
17 pages, 345 KB  
Article
Polycyclic Codes and Their Application in Constructing AEAQECCs
by Juan Li, Yunbo Tian and Fanghui Ma
Axioms 2026, 15(2), 110; https://doi.org/10.3390/axioms15020110 - 2 Feb 2026
Viewed by 523
Abstract
In this article, we study polycyclic codes over the ring R=Fq[v]/⟨v2−1⟩, where q=pm with p being an odd prime. First, we introduce polycyclic codes and sequential [...] Read more.
In this article, we study polycyclic codes over the ring R=Fq[v]/⟨v2−1⟩, where q=pm with p being an odd prime. First, we introduce polycyclic codes and sequential codes over R, and characterize the structural properties of these polycyclic codes. Next, we analyze the Euclidean dual codes, annihilator dual codes, annihilator self-orthogonal codes, and annihilator linear complementary dual (LCD) codes associated with this family of codes. Finally, some asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) are constructed from polycyclic codes over R. Moreover, the parameters of our AEAQECCs are new in the existing literature. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
24 pages, 367 KB  
Article
Factorizations in Geometric Lattices
by Alex Aguila, Elvis Cabrera and Jyrko Correa-Morris
Axioms 2025, 14(7), 483; https://doi.org/10.3390/axioms14070483 - 21 Jun 2025
Viewed by 1221
Abstract
This article investigates atomic decompositions in geometric lattices isomorphic to the partition lattice Π(X) of finite set X, a fundamental structure in lattice theory and combinatorics. We explore the role of atomicity in these lattices, building on concepts introduced [...] Read more.
This article investigates atomic decompositions in geometric lattices isomorphic to the partition lattice Π(X) of finite set X, a fundamental structure in lattice theory and combinatorics. We explore the role of atomicity in these lattices, building on concepts introduced by D.D. Anderson, D.F. Anderson, and M. Zafrullah within the context of factorization theory in commutative algebra. As part of the study, we first examine the main characteristics of the function N:Π(X)→N, which assigns to each partition π the number of minimal atomic decompositions of π. We then consider a distinguished subset of atoms, R, referred to as the set of red atoms, and derive a recursive formula for π(X,j,s,R), which enumerates the rank-j partitions expressible as the join of exactly s red atoms. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
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35 pages, 382 KB  
Article
Generalized Pauli Fibonacci Polynomial Quaternions
by Bahadır Yılmaz, Nazmiye Gönül Bilgin and Yüksel Soykan
Axioms 2025, 14(6), 449; https://doi.org/10.3390/axioms14060449 - 6 Jun 2025
Cited by 1 | Viewed by 1492
Abstract
Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies. This paper introduces the generalized notion of Pauli Fibonacci polynomial quaternions, [...] Read more.
Since Hamilton proposed quaternions as a system of numbers that does not satisfy the ordinary commutative rule of multiplication, quaternion algebras have played an important role in many mathematical and physical studies. This paper introduces the generalized notion of Pauli Fibonacci polynomial quaternions, a definition that incorporates the advantages of the Fibonacci number system augmented by the Pauli matrix structure. With the concept presented in the study, it aims to provide material that can be used in a more in-depth understanding of the principles of coding theory and quantum physics, which contribute to the confidentiality needed by the digital world, with the help of quaternions. In this study, an approach has been developed by integrating the advantageous and consistent structure of quaternions used to solve the problem of system lock-up and unresponsiveness during rotational movements in robot programming, the mathematically compact and functional form of Pauli matrices, and a generalized version of the Fibonacci sequence, which is an application of aesthetic patterns in nature. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
13 pages, 222 KB  
Article
Notes on Semiprime Ideals with Symmetric Bi-Derivation
by Ali Yahya Hummdi, Öznur Gölbaşı, Emine Koç Sögütcü and Nadeem ur Rehman
Axioms 2025, 14(4), 260; https://doi.org/10.3390/axioms14040260 - 29 Mar 2025
Cited by 1 | Viewed by 704
Abstract
In this paper, we prove many algebraic identities that include symmetric bi-derivation in rings which contain a semiprime ideal. We intend to generalize previous results obtained for semiprime rings with symmetric derivation using semiprime ideals in rings. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
17 pages, 383 KB  
Article
An Exploration of Ideals and Filters in Triangle Algebras
by Euclide Noumen, Fabrice Tchoua Yinga, Blaise Blériot Koguep Njionou and Chris Cornelis
Axioms 2024, 13(8), 566; https://doi.org/10.3390/axioms13080566 - 21 Aug 2024
Cited by 2 | Viewed by 1401
Abstract
In the study of algebraic structures related to logical systems, ideals and filters have different meanings and are algebraic notions related to logical provable formulas. Unlike the classical Boolean lattice theory, ideals and filters are not dual notions in residuated lattices. An interesting [...] Read more.
In the study of algebraic structures related to logical systems, ideals and filters have different meanings and are algebraic notions related to logical provable formulas. Unlike the classical Boolean lattice theory, ideals and filters are not dual notions in residuated lattices. An interesting subclass of residuated lattices is the class of triangle algebras, which is an equational representation of interval-valued residuated lattices that provides an algebraic framework for using closed intervals as truth values in fuzzy logic. The main aim of this article is to introduce and study the concept of ideals in triangle algebras and investigate the connection between ideals and filters. We first point out that the construction procedure for the filter generated by a subset of a triangle algebra established by another study is incorrect, and we proceed to give an alternative characterization. Full article
(This article belongs to the Special Issue Advances in Applied Algebra and Related Topics)
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