Abstract
In this article, we introduce the concepts of quasi g - NE -semicommutative rings and homogeneous quasi g - NE -semicommutative rings. Let G be a group, R be a G-graded ring and g is an element of supp.R, G.. If N.R. and E.R., respectively, denote the set of nilpotent elements and the set of idempotent elements of R, then R is said to be quasi g. NE -semicommutative if whenever a is an element of N. R. and b is an element of E.R. such that ab. 0, then baR(g)b = 0. R is said to be homogeneous quasi g. NE -semicommutative if N(R) subset of R-g and for all a is an element of N(R) and b is an element of h(R) boolean AND E(R), ba is an element of N(R). Several properties and results concerning quasi g. NE -semicommutative rings and homogeneous quasi g. NE -semicommutative rings have been discussed and established. Also, we provide various examples based on rings of matrices to illustrate these concepts.