Semi-commutativity of graded rings and graded modules

A ring R is said to be semi-commutative if whenever a, b ∈ such that ab = 0, then aRb 0. In this article, we introduce the concepts of g−semi-commutative rings and g−N−semi-commutative several results concerning these two concepts. Let a G-graded g supp(R, G). Then with aRgb Also, − N−semi-commutative for any N(R) ⋂ Ann(a), bRg ⊆ Ann(a). We an example which N-semi-commutative some G) but itself not semi-commutative. Clearly, ring, however, showing converse true in general. Several examples are investigated. concept NE−semi-commutative g−NE−semi-commutative rings. g−NE− E(R) −NE−semi-commutative, ...