The strong Mori property in rings with zero divisors
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1285-1295
https://doi.org/10.4134/BKMS.2015.52.4.1285
Published online July 31, 2015
Dechuan Zhou and Fanggui Wang
Sichuan Normal University, Sichuan Normal University
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.
Keywords : $Q_{0}$-SM ring, semiregular $w$-ideal, semiregular $v$-ideal
MSC numbers : 13A15, 13F05
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd