JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE STRONG MORI PROPERTY IN RINGS WITH ZERO DIVISORS
ZHOU, DECHUAN; WANG, FANGGUI;
  PDF(new window)
 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 -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 -SM rings are discussed and examples are provided to show the difference between -SM rings and SM rings and the difference between -SM rings and -Mori rings.
 Keywords
-SM ring;semiregular w-ideal;semiregular v-ideal;
 Language
English
 Cited by
 References
1.
J. Huckaba, Commutative Rings with Zero Divisors, Dekker, New York, 1988.

2.
C. J. Hwang and J. W. Lim, A note on $*_w$-Noetherian domains, Proc. Amer. Math. Soc. 141 (2013), no. 4, 1199-1209.

3.
T. G. Lucas, Strong Prufer rings and the ring of finite fraction, J. Pure Appl. Algebra 84 (1993), no. 1, 59-71. crossref(new window)

4.
T. G. Lucas, The integral closure of R(X) and RhXi, Comm. Algebra 25 (1997), no. 3, 847-872. crossref(new window)

5.
T. G. Lucas, The Mori property in rings with zero divisors, Rings, modules, algebras, and abelian groups, 379-400, Lecture Notes in Pure and Appl. Math., 236, Dekker, New York, 2004.

6.
J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.

7.
F. G. Wang, Finitely presented type modules and w-coherent rings, J. Sichuan Normal Univ. 33 (2010), 1-9.

8.
F. G. Wang and R. L. McCasland, On w-modules over strong Mori domains, Comm. Algebra 25 (1997), no. 4, 1285-1306. crossref(new window)

9.
F. G. Wang and R. L. McCasland, On strong Mori domains, J. Pure Appl. Algebra 135 (1999), no. 2, 155-165. crossref(new window)

10.
H. Y. Yin, F. G. Wang, X. S. Zhu, and Y. H. Chen, w-modules over commutative rings, J. Korean Math. Soc. 48 (2011), no. 1, 207-222. crossref(new window)