【摘要】 本文刻画了零可换环的一些性质,同时将交换环上的一些结果推广到零可换环上.对于零可换环R 证明了: (1)R是强正则环当且仅当R中每个为零化子的本质左理想是左GP.内射模或R中存在一个极大左理想K,使得K中每个元索的零化子是左GP-内射模; (2)R是GPP-环当且仅当R是拟π-正则的GPF-环.更多还原

【Abstract】 This paper investigates some properties of zero commutative rings and extend some results from commutative rings to zero commutative rings. If R is a zero commutative ring, the authors obtain that (1) R is strongly regular if and only if every essential left ideal of R which is an annihilator is left GP-injective or R contains a maximal left ideal K such that the annihilator of every element of K is left GP-injective; (2) R is a GPP-ring if and only if it is a quasi π-regular ring and GPF-ring.更多还原