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On multiplicative (generalized) - derivations and central valued conditions in prime rings

Sandhu Gurninder S., Ayran Ayşe, Aydin Neşet

Journal of Mathematics and Applications

2021

Vol. 44

93--105

Let R be a prime ring with multiplicative (generalized)- derivations (F, f) and (G, g) on R. This paper gives a number of central valued algebraic identities involving F and G that are equivalent to the commutativity of R under some suitable assumptions. Moreover, in order to optimize our results, we show that the assumptions taken cannot be relaxed.

Some results on 2-absorbing ideals in commutative semirings

Kumar P., Dubey M. K., Sarohe P.

Journal of Mathematics and Applications

2015

Vol. 38

77--84

In this paper, we study the concepts of 2-absorbing and weakly 2-absorbing ideals in a commutative semiring with non-zero identity which is a generalization of prime ideals of a commutative semiring and prove number of results related to the same. We also use these concepts to prove some results of Q-ideals in terms of subtractive extension of ideals in a commutative semiring.

Notes on the ideal-based zero-divisor graph

Yousefian D.

Journal of Mathematics and Applications

2010

Vol. 32

103-107

Let I be an ideal of a commutative ring R. Denote by S(I) the set {x ∈ R | xy ∈ I for some y ∈ R \ I}. The zero-divisor graph of R with respect to I is an undirected graph, denoted by [wzór], with vertices S(I) \ I where distinct vertices x and y are adjacent if and only if xy ∈ I. In this paper we study the diameter and the girth of [wzór], when the prime ideals of R contained in S(I) are linearly ordered.