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Characterizations and Direct Sums of Unit-Endoregular Modules
Published online by Cambridge University Press: 10 August 2018
Abstract
A module is called unit-endoregular if its endomorphism ring is unit-regular. In this paper, we continue the research in unit-endoregular modules. More characterizations of unit-endoregular modules are obtained. As a special case, we show that for an abelian group G, Endℤ(G) is a unit-regular Baer ring if and only if Endℤ(G) is a two-sided extending regular ring. While the class of unit-endoregular modules is not closed under direct sums, we provide a characterization when there are direct sums of two or more unit-endoregular modules also unit-endoregular under certain conditions. In particular, we investigate unit-endoregular modules which are direct sums of indecomposable modules.
Keywords
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 1103 - 1112
- Copyright
- Copyright © Edinburgh Mathematical Society 2018