Galois Journal of Algebra

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1. Call for Papers-Special Issue on Recent Advances in Algebraic Graph Theory

2. Call for Papers-Special Issue on Recent Advances in Monomial Algebras

3. Call for Papers-Special Issue on Recent Advances in Algebraic Combinatorics

4. Call for Papers-Special Issue on Algebraic Coding Theory and Cryptography

Welcome to the Galois Journal of Algebra

The Galois Journal of Algebra (GJA), with online ISSN 3099-196X, is an international, peer-reviewed, open access electronic academic journal, published exclusively online and dedicated to publishing original research and high-quality expository articles in all areas of algebra. Named in honor of Évariste Galois, whose pioneering work laid the foundation of modern algebra, the journal seeks to uphold his legacy by promoting deep and innovative contributions to the field. In particular, GJA publishes comprehensive review articles that offer insights into current developments.

For all correspondence, please contact the journal at https://gja.intrasci.net/journal/contact.us.

The journal is devoted to publication of original significant research articles including but not limited to

◉ Group theory and representation theory (MSC 20C, 20D, 20E)
◉ Ring theory and module theory (MSC 16D, 16E, 13C)
◉ Field theory and Galois theory (MSC 12F, 12E)
◉ Commutative algebra and related topics (MSC 13A, 13B, 13D)
◉ Noncommutative algebra and related topics (MSC 16K, 16L, 16S)
◉ Homological algebra and related topics (MSC 18G, 16E05)
◉ Algebraic geometry (MSC 14A, 14F, 14G)
◉ Algebraic coding theory and Cryptography (MSC 94B, 94A60)
◉ Algebraic topology (MSC 55N, 55P, 55Q)
◉ Linear algebra and its applications (MSC 15A, 15B)
◉ Algebraic combinatorics (MSC 05E)
◉ Algebraic graph theory (MSC 05C)
◉ Algebraic number theory (MSC 11R, 11S)
◉ Lie algebras (MSC 17B, 17C)
◉ Category theory with applications to algebra (MSC 18A, 18B)
◉ Banach algebras and C*-algebras (MSC 46H, 46L)
◉ Hopf algebras (MSC 16T)
◉ Hyperstructures in algebra and Fuzzy algebra (MSC 20N20, 20N25, 08A72)
◉ Computer algebra (MSC 68W30)
◉ Algebraic methods in AI (MSC 68Txx, 03Bxx)

 

Original Article
Essential ideal transforms

Ismael Akray; Runak Mustafa

Volume 1, Issue 1 , December 2025, Pages 1-11

Abstract
  It is our intention in this research generalize some concept in local cohomology such as free modules, contravariant functor $ext$, covariant functor $Ext$ and ideal transforms with $e$-exact sequences. The $e$-exact sequence was introduced by Akray and Zebari \cite{AZ} in 2020. we prove that essential ...  Read More
Review Article
Some Perspectives on Distribution of strongly persistent clutters

Jonathan Toledo Toledo; Enrique Reyes Espinoza

Volume 1, Issue 1 , December 2025, Pages 12-42

Abstract
  This survey aims to present and promote the study of the strong persistence property in clutters from a quantitative and structural perspective. We denote by Cn the set of all clutters on [n], by Sn the subset of clutters satisfying the SPP, and by Nn = Cn ∖ Sn those that fail it. Our analysis focuses ...  Read More
Original Article
A family of rank 4 non-algebraic matroids with pseudomodular dual

Winfried Hochstättler

Volume 1, Issue 1 , December 2025, Pages 43-50

Abstract
  The Tic-Tac-Toe matroid is a paving matroid of rank 5 on 9 ele-ments which is pseudomodular and whose dual is non-algebraic. It has beenproposed as a possible example of an algebraic matroid whose dual is not algebraic. We present an infinite family of matroids sharing these properties andgeneralizing ...  Read More
Review Article
Recent Advances in the Theory of Polyomino Ideals

Ayesha Asloob Qureshi; Francesco Navarra

Volume 1, Issue 1 , December 2025, Pages 51-87

Abstract
  Polyomino ideals, defined as the ideals generated by the inner $2$-minors of a polyomino, are a class of binomial ideals whose algebraic properties are closely related to the combinatorial structure of the underlying polyomino. We provide a unified account of recent advances on two central themes: the ...  Read More
Review Article
Advances in Arithmetic and Geometry over division rings

Elad Paran

Volume 1, Issue 1 , December 2025, Pages 88-117

Abstract
  In recent years there has been a flurry of activity surrounding non-commutative Nullstellens\"atze over the real quaternion algebra and over general division rings. From these results emerge rich arithmetic and geometry, which in many ways follow the classical themes and ideas of complex algebraic geometry, ...  Read More
Original Article
Classification, derivations and centroids of low-dimensional associative trialgebras

Bouzid Mosbahi; Imed Basdouri; Ahmed Zahari

Volume 1, Issue 1 , December 2025, Pages 118-136

Abstract
  In this paper, we study the structure and algebraic varieties of associative trialgebras. In partic-ular, we classify all associative trialgebras of dimension at most four over a field of characteristic zero. Based on this classification, we provide a detailed analysis of their derivations and centroids. ...  Read More
Review Article
Essential Dimension of Central Simple Algebras when the Characteristic is Bad

Adam Chapman; Kelly McKinnie

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose characteristic divides the degree of the algebras under discussion. Upper ...  Read More
Original Article
On the condition of the order of a periodic derivation in low dimensional complex Leibniz algebras

Nil Mansuroğlu

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  This study aims to investigate the low dimensional complex Leibniz algebras which admit a periodicderivation. The principal goal of this note is to characterize such algebras and to develope some propertieson periodic derivations. We demonstrate that finite dimensional complex Leibniz algebras admitting ...  Read More
Original Article
A complete classification of perfect unitary Cayley graphs

Jan Minac; Tung T. Nguyen; Duy Tan Nguyen

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  Due to their elegant and simple nature, unitary Cayley graphs have been an active research topic in the literature. These graphs are naturally connected to several branches of mathematics, including number theory, finite algebra, representation theory, and graph theory. In this article, we study the ...  Read More
Review Article
Pseudo-linear maps, an overview

André G. LEROY

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  In this survey we give a brief account of the history of pseudo-linear maps since their introduction by N. Jacobson in 1937.The ($\si,\de$)-pseudo-linear transformations are introduced via the modules over a skew polynomial ring.Many classical properties of linear maps are shown to have analogues in ...  Read More
Review Article
A comprehensive study on chain conditions in Rings and Modules

R. K. Singh; Manoj Kumar Patel; H Chakraborty; Meyibenla .; T Lohe

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  This survey presents a comprehensive and systematic overview of the theory of chain conditions on modules and rings with particular emphasis on injective and quasi-injective modules, as well as associated structural properties of rings. We cover classical and modern perspectives on ascending and descending ...  Read More
Review Article
An Overview of Monomorphism Categories

Rasool Hafezi

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  In this survey, the author collects and presents several of his recent results and joint works on monomorphism categories, covering various topics in representation theory. We try to show that how one can approach the monomorphism categories via functor categories. In the representation-finite case, ...  Read More
Original Article
Parametric Constructions of Monogenic and Exceptional Sextic Fields

V. Parthiban; C. Aruna

Articles in Press, Accepted Manuscript, Available Online from 25 February 2026

Abstract
  We investigate two parametric families of irreducible sextic polynomials over $\mathbb{Q}$, denoted $g(x;t)$ and $h(x;t)$, and the number fields they generate. For integers $t$ in suitable ranges, we show that the fields \[K_t = \mathbb{Q}(\alpha) \quad \text{and} \quad L_t = \mathbb{Q}(\theta),\] where ...  Read More
Galois Journal of Algebra

Publisher:
Interaction Scientifique

Editor-in-Chief:
Mehrdad Nasernejad

Managing Editor:
Mahdi Reza Khorsandi Jonathan T. Toledo

Editor:
André Leroy Alain Bretto Wieslaw A. Dudek Jan Minac Ángel del Río Peyman Nasehpour Rasool Hafezi Li Liang Manoj Kumar Patel Najib Mahdou Nil Mansuroğlu Mohammad Shahryari Ayesha Asloob Qureshi Anda Olteanu Krishnan Selvakumar Stephen Scully Patrick McFaddin Giancarlo Lucchini Arteche Thangaraj Asir Deep Singh Eric Andriantiana Ismael Akray

Language Editor:
Mazyar Ghani Varzaneh

Frequency: Quarterly

Online ISSN: 3099-196X

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Call for Papers-Special Issue on Algebraic Coding Theory and Cryptography

Call for Papers-Special Issue on Algebraic Combinatorics

Call for Papers-Special Issue on Algebraic Graph Theory

Call for Papers-Special Issue on Monomial Algebras

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