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| ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC^{\perp}ON ANNIHILATOR IDEALS. |
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Citation： |
Zhang Yinhuo.ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC^{\perp}ON ANNIHILATOR IDEALS.[J].Chinese Annals of Mathematics B,1991,12(2):152~156 |
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Net amount： 795 |
Authors： |
Zhang Yinhuo; |
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| Abstract： |
The author concludes that every commutative ring with ascending chain condition an annihilator ideals has a Kasch quotient ring, which generalizes the Theorem^{[1]} that
every commutative noetherian ring has a Kasch quosient ring. If follows that if R is a commutative ting with acc^{\perp}，then that Q(R) is semiprimary is equivalent to that it is perfect, or to that R satisfies regular condition. Besides, that Q(R) is quasi-frobenius equals that Q(R) is FPF or PF, and that Q(R) is artinian equals that R/N, are of finite dimension, i=1,2,\ldots,n. N_{i}=J^{i}\cap R. |
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