Jul 2026· Asian-European Journal of Mathematics· 0 citations
Abstract
Let [Formula: see text] be a commutative ring, and let [Formula: see text] denote the set of all nonzero elements of [Formula: see text]. The weak zero-divisor graph of [Formula: see text], denoted by [Formula: see text], is an undirected graph whose vertex set consists of the elements in [Formula: see text]. Two distinct vertices [Formula: see text] and [Formula: see text] are connected by an edge if and only if there exists a positive integer [Formula: see text] such that [Formula: see text].
In this study, we investigate finite commutative rings [Formula: see text] whose associated weak zero-divisor graphs [Formula: see text] belong to certain well-established classes of graphs. Specifically, we provide a classification of finite rings [Formula: see text] for which the graph [Formula: see text] is a unicyclic graph, a tree, a split graph, a planar graph, or an outerplanar graph. In addition, we explore the conditions under which [Formula: see text] is a toroidal graph.
Let [Formula: see text] be a ring with nonzero identity and [Formula: see text] denotes the set of idempotents in [Formula: see text]. A graph of [Formula: see text] with respect to idempotents [Formula: see text] is a graph whose vertices are elements of [Formula: see text] and two vertices [Formula: see text] and [Fo...
Dipika B. Patil, Avinash Patil· Journal of Algebra and its A...· 0 citations
Let [Formula: see text] be a grading-restricted vertex algebra, and [Formula: see text] be the algebraic completion of the space of [Formula: see text]-valued rational functions with complex parameters [Formula: see text], [Formula: see text]. We consider two subspaces [Formula: see text] and [Formula: see text] of [Fo...
A. Zuevsky· International Journal of Geo...· 0 citations
In this paper, [Formula: see text] denotes a multiplicatively closed set of a commutative ring [Formula: see text]. Then [Formula: see text]-coherent rings are introduced. A ring [Formula: see text] is called [Formula: see text]-coherent if every finitely generated [Formula: see text]-ideal of [Formula: see text] is fi...
Yudan Xiang, De-Chuan Zhou, Kui Hu· Journal of Algebra and its A...· 0 citations
A hereditary class [Formula: see text] of graphs is [Formula: see text]-bounded if there is a [Formula: see text]-binding function, say [Formula: see text], such that [Formula: see text], for every [Formula: see text], where [Formula: see text] denotes the chromatic (clique) number of [Formula: see text]. A [Formula: s...
Li Zhang, Xia Hong· Discrete Mathematics, Algori...· 0 citations
This paper is devoted to the study of graded associative algebras that satisfy a graded polynomial identity of degree [Formula: see text]. Let [Formula: see text] be a finite abelian group, [Formula: see text] a field of characteristic zero and [Formula: see text] a [Formula: see text]-graded [Formula: see text]-algebr...
Antonio de França· Journal of Algebra and its A...· 0 citations
Graphs whose edge rings have regularity two are not completely characterized. We, therefore, study the minimal graded free resolution of edge rings of certain families of graphs, such as the general barbell graph [Formula: see text] (or [Formula: see text]-barbell graph) and the complete [Formula: see text]-sunlet grap...
Shahnawaz Ahmad Rather, S. Pirzada· Algebra Colloquium· 0 citations
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