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
Volume 1 (2025)
Number of Articles: 6
Essential ideal transforms
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 MoreSome Perspectives on Distribution of strongly persistent clutters
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 MoreA family of rank 4 non-algebraic matroids with pseudomodular dual
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 MoreRecent Advances in the Theory of Polyomino Ideals
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 MoreAdvances in Arithmetic and Geometry over division rings
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 MoreClassification, derivations and centroids of low-dimensional associative trialgebras
Volume 1, Issue 1 , December 2025, Pages 118-136