半替换环和半局部环的K_1-群(英文)

SEMIEXCHANGE RIGNS AND K_1-GROUPS OF SEMILOCAL RINGS

本文定义环R为半替换环如果R/J(R)为替换环,它是替换环和半局部环的共同推广．研究了半替换环的一些性质,并回答了[8]中半局部环K_1-群的一个问题．

A ring R in this note is defined to be a semiexchange ring if R/J（R） is an exchange ring which is a common generalization of an exchange ring and a semilocal ring. Some properties of semiexchange rings are investigated. Also we answer a question posed in [8] on K1-groups of semilocal rings.