摘要
设R是一个含幺结合环 .如果任意两个稳定同构的有限生成投射R 模均是同构的 ,则称R是强Hermitian环 ;如果对任意正则元a ,b∈R且aR+bR =R ,均存在y∈R使得a+by可逆 ,则称R是正则地稳定环 .本文证明了环R是强Hermitian环 ,当且仅当对任意自然数n有Mn(R)是正则地稳定环 .
A ring R is defined to be strong Hermitian if a ny two stablely isomorphic finitely generated projective R-module s are isomorphic; and to be regularly stable if for any regular elements a a nd b in R, aR+bR=R implies that there exists y∈R such that a+by is invertible. It is proved that R is strong Hermitian iff M n (R) i s regularly stable for any natural integer n. Some characterizations of reg ularly stable rings are given.
关键词
K0群
模的稳定同构
内消去性
正则地稳定环
K 0 group
stable isomorphism of module s
internal-cancellation property
regularly stable rings CLC number:O153 Document code:A AMS Subject Classifications (2000): 19A13
