Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings
Copyright policy )Zero-Divisor Graphs with respect to Ideals in Noncommutative Rings
Let R be a commutative ring and I an ideal of R. The zero-divisor graph of R with respect to I, denoted ΓI(R), is the undirected graph whose vertex set is {x∈R∖I|xy∈I for some y∈R∖I} with two distinct vertices x and y joined by an edge when xy∈I. In this paper, we extend the definition of the ideal-based zero-divisor graph to noncommutative rings.
- University of Guilan Iran (Islamic Republic of)
- University of Mohaghegh Ardabili Iran (Islamic Republic of)
Conditions on elements, diameters, ideal-based zero-divisor graphs, primal ideals, prime ideals, zero-divisors, Ideals in associative algebras, Graphs and abstract algebra (groups, rings, fields, etc.)
Conditions on elements, diameters, ideal-based zero-divisor graphs, primal ideals, prime ideals, zero-divisors, Ideals in associative algebras, Graphs and abstract algebra (groups, rings, fields, etc.)
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