A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorph...A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.展开更多
In this paper,we study the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincare–Birkhoff–Witt extensions.As a consequence,we generalize several results about this no...In this paper,we study the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincare–Birkhoff–Witt extensions.As a consequence,we generalize several results about this notion considered in the literature for commutative rings and Ore extensions.展开更多
基金The NSF(11071097,11101217)of Chinathe NSF(BK20141476)of Jiangsu Province
文摘A weakly 2-primal ring is a common generalization of a semicommutative ring, a 2-primal ring and a locally 2-primal ring. In this paper, we investigate Ore extensions over weakly 2-primal rings. Let α be an endomorphism and δ an α- derivation of a ring R. We prove that （1） If R is an （α, δ）-compatible and weakly 2-primal ring, then R[x; α, δ] is weakly semicommutative; （2） If R is （α, δ）-compatible, then R is weakly 2-primal if and only if R[x; α, δ] is weakly 2-primal.
基金Research is supported by Grant HERMES CODE 30366Departamento de Matemati-cas,Facultad de Ciencias,Universidad Nacional de Colombia,Sede Bogota.
文摘In this paper,we study the notion of McCoy ring over the class of non-commutative rings of polynomial type known as skew Poincare–Birkhoff–Witt extensions.As a consequence,we generalize several results about this notion considered in the literature for commutative rings and Ore extensions.
