Taiwanese Journal of Mathematics

MODULES WHOSE CLOSED SUBMODULES WITH ESSENTIAL SOCLE ARE DIRECT SUMMANDS

Septimiu Crivei and Serap Şahinkaya

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Abstract

We introduce and study CLESS-modules, which subsume two generalizations of extending modules due to P.F. Smith and A. Tercan. A module $M$ will be called a CLESS-module if every closed submodule $N$ of $M$ (in the sense that $M/N$ is non-singular) with essential socle is a direct summand of $M$. Various properties concerning direct sums of CLESS-modules are established. We show that, over a Dedekind domain, a module is CLESS if and only if its torsion submodule is a direct summand. We also study the behaviour of CLESS-modules under excellent extensions of rings.

Article information

Source
Taiwanese J. Math., Volume 18, Number 4 (2014), 989-1002.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706472

Digital Object Identifier
doi:10.11650/tjm.18.2014.3388

Mathematical Reviews number (MathSciNet)
MR3245425

Zentralblatt MATH identifier
1357.16011

Subjects
Primary: 16D10: General module theory 16P70: Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence

Keywords
extending module (CS-module) CESS-module CLS-module CLESS-module complement closed submodule socle (non-)Singular module

Citation

Crivei, Septimiu; Şahinkaya, Serap. MODULES WHOSE CLOSED SUBMODULES WITH ESSENTIAL SOCLE ARE DIRECT SUMMANDS. Taiwanese J. Math. 18 (2014), no. 4, 989--1002. doi:10.11650/tjm.18.2014.3388. https://projecteuclid.org/euclid.twjm/1499706472


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