Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS

  • ZHOU, DECHUAN (COLLEGE OF MATHEMATICS AND SOFTWARE SCIENCE SICHUAN NORMAL UNIVERSITY) ;
  • WANG, FANGGUI (COLLEGE OF MATHEMATICS AND SOFTWARE SCIENCE SICHUAN NORMAL UNIVERSITY)
  • Received : 2014.09.01
  • Published : 2015.07.31
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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 $Q_0$-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 $Q_0$-SM rings are discussed and examples are provided to show the difference between $Q_0$-SM rings and SM rings and the difference between $Q_0$-SM rings and $Q_0$-Mori rings.

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References

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