In this article, we introduce the concepts of quasi -semi-commutative rings and homogeneous quasi -semi-commutative rings. Let G be a group, R be a G-graded ring and  If  and  respectively, denote the set of nilpotent elements and the set of idempotent elements of R, then R is said to be quasi -semicommutative if whenever  and  such that  then  R is said to be homogeneous quasi -semicommutative if  and for all  and  Several properties and results concerning quasi -semicommutative rings and homogeneous quasi -semicommutative rings have been discussed and established. Also, we provide various examples based on rings of matrices to illustrate these concepts.

semicommutativity of graded rings, -semicommutative rings, quasi -semicommutative rings, homogeneous quasi -semicommutative rings, g-directly finite rings.

Received: June 15, 2021; Accepted: July 28, 2021; Published: August 21, 2021

How to cite this article: Hicham Saber, Tariq Alraqad and Rashid Abu-Dawwas, Quasi -semicommutative rings, JP Journal of Algebra, Number Theory and Applications 52(1) (2021), 101-114. DOI: 10.17654/NT052010101

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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