We introduce nil 3-Armendariz rings, which are generalization of 3-Armendariz rings and nil Armendaiz rings and investigate their properties. We show that a ring R is nil 3-Armendariz ring if and only if for any , Tn(...We introduce nil 3-Armendariz rings, which are generalization of 3-Armendariz rings and nil Armendaiz rings and investigate their properties. We show that a ring R is nil 3-Armendariz ring if and only if for any , Tn(R) is nil 3-Armendariz ring. Also we prove that a right Ore ring R is nil 3-Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result, we can show that a commutative ring R is nil 3-Armendariz if and only if the total quotient ring of R is nil 3-Armendariz.展开更多
Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized p...Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.展开更多
In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
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
文摘We introduce nil 3-Armendariz rings, which are generalization of 3-Armendariz rings and nil Armendaiz rings and investigate their properties. We show that a ring R is nil 3-Armendariz ring if and only if for any , Tn(R) is nil 3-Armendariz ring. Also we prove that a right Ore ring R is nil 3-Armendariz if and only if so is Q, where Q is the classical right quotient ring of R. With the help of this result, we can show that a commutative ring R is nil 3-Armendariz if and only if the total quotient ring of R is nil 3-Armendariz.
文摘Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.
文摘In this paper, we give an answer to an open p roblem which was proposed in . We show that the supersemiprime radical is e qual to the near nil radical which was defined by XIE Bang_jie in .
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.
