THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS
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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 Q0-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 Q0-SM rings are discussed and examples are provided to show the difference between Q0-SM rings and SM rings and the difference between Q0-SM rings and Q0-Mori rings.
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 Q0-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 Q0-SM rings are discussed and examples are provided to show the difference between Q0-SM rings and SM rings and the difference between Q0-SM rings and Q0-Mori rings.
참고문헌 (10)
- J. Huckaba, "Commutative Rings with Zero Divisors" (1988), Dekker
- C. J. Hwang, "A note on ∗w-Noetherian domains", Proc. Amer. Math. Soc, 141(4), pp.1199~1209 (2013)
- T. G. Lucas, "Strong Pr¨ufer rings and the ring of finite fraction", J. Pure Appl. Algebra, 84(1), pp.59~71 (1993)
- T. G. Lucas, "The integral closure of R(X) and R〈X〉", Comm. Algebra, 25(3), pp.847~872 (1997)
- T. G. Lucas, "The Mori property in rings with zero divisors, Rings, modules, algebras, and abelian groups", Lecture Notes in Pure and Appl. Math, 236, pp.379~400 (2004), Dekker
- J. J. Rotman, "An Introduction to Homological Algebra" (1979), Academic Press
- F. G. Wang, "Finitely presented type modules and w-coherent rings", J. Sichuan Normal Univ, 33, pp.1~9 (2010)
- F. G. Wang, "On w-modules over strong Mori domains", Comm. Algebra, 25(4), pp.1285~1306 (1997)
- F. G. Wang, "On strong Mori domains", J. Pure Appl. Algebra, 135(2), pp.155~165 (1999)
- Huayu Yin, "ω-MODULES OVER COMMUTATIVE RINGS", 대한수학회지, 48(1), pp.207~222 (2011), 대한수학회