THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS

Title & Authors
THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS
ZHOU, DECHUAN; WANG, FANGGUI;

Abstract
An SM domain is an integral domain which satisfies the ascending chain condition on w-ideals. Then an SM domain also satisfies the descending chain condition on those chains of v-ideals whose intersection is not zero. In this paper, a study is begun to extend these properties to commutative rings with zero divisors. A $\small{Q_0}$-SM ring is defined to be a ring which satisfies the ascending chain condition on semiregular w-ideals and satisfies the descending chain condition on those chains of semiregular v-ideals whose intersection is semiregular. In this paper, some properties of $\small{Q_0}$-SM rings are discussed and examples are provided to show the difference between $\small{Q_0}$-SM rings and SM rings and the difference between $\small{Q_0}$-SM rings and $\small{Q_0}$-Mori rings.
Keywords
$\small{Q_0}$-SM ring;semiregular w-ideal;semiregular v-ideal;
Language
English
Cited by
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