Feckly McCoy环和feckly Armendariz环

Feckly McCoy and feckly Armendariz rings

讨论了feckly McCoy环和feckly Armendariz环的各类扩张性质,证明了:(1)设R是一个feckly Armendariz环,满足J(R[x])=J(R)[x]。如果对每一个主右理想pR■J(R),存在a∈J(R)使得rJ_(R)(pR)=aR,则对每一个主右理想f(x)R[x]■J(R[x]),rJ_(R[x])(f(x)R[x])是由R[x]的Jacobson根中一个元素生成的理想。(2)设R是一个feckly约化环,满足J(R[x])=J(R)[x],则R是一个右J-APP-环当且仅当多项式环R[x]是右J-APP-环。深化了这两个新环类的研究。

To discuss the various extension properties of feckly McCoy rings and feckly Armendariz rings, it is proved that(1) let R be a feckly Armendariz ring with J(R[x])=J(R)[x], if for each principal right ideal pR■J(R), rJ(pR)=aR where a∈J(R), then for each principal right ideal f(x)R[x]■J(R[x]), rJ_(R)(f(x)R[x]) is generated as an ideal by an element which is in the Jacobson radical of R[x].(2) let R be a feckly reduced ring with J(R[x])=J(R)[x], R is a right J-APP-ring if and only if R[x] is a right J-APP-ring. These deepen the study of these two new classes of rings.