On finitely embedded rings
作者:
W.K. Nicholson,
M.F. Yousif,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 11
页码: 5311-5315
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008827157
出版商: Gordon and Breach Science Publishers Ltd.
关键词: Finitely embedded rings;annihilators;artinian rings;quasi-Frobenius rings;16D50;16L60;16P20;16P40;16P60
数据来源: Taylor
摘要:
A result of Ginn and Moss asserts that a left and right noetherian ring with essential right socle is left and right artinian. There are examples of right finitely embedded rings with ACC on left and right annihilators which are not artinian. Motivated by this, it was shown by Faith that a commutative, finitely embedded ring with ACC on annihilators (and square-free socle) is artinian (quasi-Frobenius).AringRis called right minsymmetric if, wheneverkRis a simple right ideal ofR, thenRkis also simple. In this paper we show that a right noetherian right minsymmetric ring with essential right socle is right artinian. As a consequence we show that a ring is quasi-Frobenius if and only if it is a right and left mininjective, right finitely embedded ring with ACC on right annihilators. This extends the known work in the artinian case, and also extends Faith's result to the non-commutative case.
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