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A Lattice Isomorphism Theorem for Nonsingular Retractable Modules

Published online by Cambridge University Press:  20 November 2018

Zhou Zhengping
Zhou Zhengping*
Affiliation:
Department of Mathematics University of Iowa Iowa City, Iowa 52242 U.S.A.
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Abstract

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Let RM be a nonsingular module such that B = EndR(M) is left nonsingular and has as its maximal left quotient ring, where is the injective hull of RM. Then it is shown that there is a lattice isomorphism between the lattice C(M) of all complement submodules of RM and the lattice C(B) of all complement left ideals of B, and that RM is a CS module if and only if B is a left CS ring. In particular, this is the case if RM is nonsingular and retractable.

Keywords

16D8016S90
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 1 , 01 March 1994 , pp. 140 - 144
Copyright
Copyright © Canadian Mathematical Society 1994

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