ORE EXTENSIONS OF NIL-SEMICOMMUTATIVE RINGS

In this paper, we study the properties of Ore extensions of nil-semicommutative rings. Let α be an endomorphism and δ an α -derivation of a ring R . By using the itemized analysis method on polynomials, we prove that if R is ( α , δ )-skew Armendariz and ( α , δ )-compatible, then R [ x ; α , δ ] is nil-semicommutative if and only if R is nil-semicommutative; if R is nil-semicommutative and ( α , δ )-compatible, then R [ x ; α , δ ] is weak Armendariz, which generalize some related work on skew polynomial rings.