4th International Conference on Pure and Applied Mathematics, Van, Turkey, 22 - 23 June 2022, pp.117
Semicommutative rings are a generalization of reduced rings, and thus, nilpotent elements play an important role in these rings. There are many examples of rings with nilpotent elements which are semicommutative ring. We introduce the notion of nilpotent-semicommutative rings which is a generalization of semicommutative rings. A ring R said to be a nilpotent-semicommutative ring if ∀ a, b ∈ R, ab = 0 implies aN (R)b = 0. where N (R) stands for the set of nilpotents of R. A lot of properties of nilpotent-semicommutative rings are introduced and many known results on semicommutative rings are extended.