ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC⊥ON ANNIHILATOR IDEALS |
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引用本文: | 张印火.ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC⊥ON ANNIHILATOR IDEALS[J].数学年刊B辑(英文版),1991(2). |
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作者姓名: | 张印火 |
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作者单位: | Iustitute of |
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摘 要: | The author concludes that every commutative ring with ascending chain conditionan annihilator ideals has a Kasch quotient ring,which generalizes the Theorem thatevery commutative noetherian ring has a Kasch quosient ring.If follows that if R is acommutative ring with acc~⊥,then that Q(R)is semiprimary is equivalent to that it isperfect,or to that R satisfies regular condition.Besides,that Q(R)is quasi-frobeniusequals that Q(R)is FPF or PF,and that Q(R)is artinian equals that B/N,are of finitedimension,i=1,2,…,n.N_i,=J~i∩R.
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