JTTC环的一些性质

Some properties of JTTC rings

研究JTTC环的一些性质,主要证明了如下结果:1)R是交换约化环当且仅当G3(R)是JTTC环;2)R是CN环当且仅当W4(R)是JTTC环;3)设R是JTTC环,M是R的极大左理想,a∈R,e∈E(R),则1-ae∈M当且仅当1-ea∈M;4)R是JTTC环当且仅当对R的每个Pierce理想P,有R/P是JTTC环.

In this paper, some properties of JTTC rings are discussed, and the following results for a JTTC ring R are mainly shown. 1） R is a commutative reduced ring if and only if G3 （R） is a JTTC ring. 2） R is a CN ring if and only if W4 （R） is a JTTC ring. 3） Let R be a JTTC ring, M be a max- imal left ideal ofR andaER, eEE（R）, then 1--ae∈M if and only if 1--ea∈M. 4） R is a JTTC ring if and only if for every Pierce ideal P of R, R/P is a JTTC ring.