Feckly McCoy环

Feckly McCoy Rings

本文引进一类新环——feckly McCoy环.一个环R称为右feckly McCoy环,如果商环R/J(R)是右McCoy环.我们讨论右feckly McCoy环与相关环之间的关系,研究它们的Ore扩张,给出J-零化子的一些应用.证明了:(1)如果R是一个弱2-素δ-相容环,J(R)是诣零的,其中δ是环R的一个导子使得δ(J(R))⊆J(R),则R是右feckly McCoy的当且仅当R[x;δ]是右feckly McCoy的;(2)如果R是一个右feckly McCoy环,且J(R[x])=J(R)[x],则R是右J-zip的当且仅当R[x]是右J-zip的.

This article introduces a new class of rings called right feckly McCoy rings.A ring R is called right feckly McCoy if R/J(R)is a right McCoy ring.We discuss the relationship between right feckly McCoy rings and related rings,investigate their Ore extensions and give some applications to J-annihilators.It is proved that(1)if R is a weakly 2-primalδ-compatible ring and J(R)is nil,whereδis a derivation of R such thatδ(J(R))⊆J(R),then R is right feckly McCoy if and only if R[x;δ]is right feckly McCoy;(2)if J(R[x])=J(R)[x],where R is a right feckly McCoy ring,then R is right J-zip if and only if R[x]is right J-zip.