In this paper we investigate 3-prime near-rings with generalized two sided α -derivations satisfying certain differential identities. Consequently, some well known results have been generalized. Moreover, an example proving the necessity of the 3-primeness hypothesis is given. [ABSTRACT FROM AUTHOR]
In the present paper it is shown that 3-prime left near-rings satisfying certain identities involving generalized derivations are commutative rings. Moreover, examples proving the necessity of the 3-primeness hypothesis in various theorems are given. [ABSTRACT FROM AUTHOR]
Ashraf, Mohammad, Siddeeque, Mohammad Aslam, and Parveen, Nazia
Abstract
A non-empty subset U of a near-ring N is said to be a semigroup left (resp. right) ideal of N if NU ⊆ U (resp. UN ⊆ U ) and if U is both a semigroup left ideal and a semigroup right ideal, it will be called a semigroup ideal. In the present paper, we investigate the commutativity of addition and multiplication of near-rings satisfying certain identities involving n -derivations on semigroup ideals and ideals. Furthermore, we study the conditions with semigroup ideals for n -derivations D 1 and D 2 of N which imply that D 1 = D 2 . [ABSTRACT FROM AUTHOR]
Ashraf, Mohammed, Boua, Abdelkarim, and Raji, Abderrahmane
Abstract
In the present paper it is shown that zero symmetric prime right near-rings satisfying certain identities are commutative rings. [ABSTRACT FROM AUTHOR]