Classification of Rings with Toroidal and Projective Coannihilator Graph

Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS or β∉αβS, where δS denotes the principal idea...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2021; pp. 1 - 7
Main Authors Alanazi, Abdulaziz M., Nazim, Mohd, Ur Rehman, Nadeem
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 01.01.2021
Hindawi Limited
Subjects
Commutativity
Graphs
Mathematics
Rings (mathematics)
Theorems
Vertex sets
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Summary:Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS or β∉αβS, where δS denotes the principal ideal generated by δ∈S. In this study, we first classify finite ring S, for which AG′S is isomorphic to some well-known graph. Then, we characterized the finite ring S, for which AG′S is toroidal or projective.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/4384683