On the Zero Divisor Graphs of Finite Rings in Which the Product of Any Two Zero Divisors Lies in the Coefficient Subring
Walwenda Shadrack Adero, Ingado Daisy, Owino Maurice Oduorand project Le-MATH partners
Abstract: Let r be a positive integer and 2≤k∈Z. Let GR(pkr, pk) be a Galois ring of order pkr and characteristic pk. Consider, R = GR(pkr, pk) ⊕U where U is a finitely generated GR(pkr, pk) module. If Z(R) is the set of zero divisors in R satisfying the condition then it is well known that R is a completely primary finite ring and the structure of its group of units has been studied before. In this paper, we study the structure of its zero divisors via the zero divisor graphs.
Keywords: Finite rings, Zero divisor graphs.
Pages: 524 – 533 | Full PDF Paper