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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.

Identities with two automorphisms on semiprime rings

Kosi-Ulbl I.

Demonstratio Mathematica

2007

Vol. 40, nr 1

37-42

In this paper we investigate identities with two automorphisms on semiprime rings. We prove the following result: Let T, S : R approaches R be automorphisms where R is a 2-torsion free semiprime ring satisfying the relation T(x)x = xS(x) for all x is an element of R. In this case the mapping x approaches T(x) - x maps R into its center and T = S.

On alfa-derivations of prime and semiprime rings

Vukman J.

Demonstratio Mathematica

2005

Vol. 38, nr 2

283--290

In this paper we investigate identities with alfa-derivations on prime and semiprime rings. We prove, for example, the following result. If D : R - R is an alfa-derivation of a 2 and 3-torsion free semiprime ring R such that [D(x},x2] = 0 holds, for all x is an element of R, then D maps R into its center. The results of this paper are motivated by the work of Thaheem and Samman [20].