# On A Class of Semicommutative Rings

### New Zealand Journal of Mathematics

Vol. 47, (2017), Pages 69-85

Abdullah Harmanci

Department of Mathematics,

Hacettepe University,

Turkey

Handan Kose

Department of Mathematics,

Ahi Evran University,

Turkey

Abstract Let R be a ring with identity and an ideal $I$. In this paper, we introduce a class of rings generalizing semicommutative rings which is called I-semicommutative. The ring R is called I-semicommutative whenever ab = 0 implies $aRb\subseteq I$ for any $a, b\in R$. We investigate general properties of I-semicommutative rings and show that several results of semicommutative rings and J-semicommutative rings can be extended to I-semicommutative rings for this general settings.

Keywords Semicommutative rings, J-Semicommutative rings, I-Semicommutative rings, Exchange rings, Ideal extensions, Nil Semicommutative rings.

Classification (MSC2000) 13C99, 16D80, 16U80.