Characterizations and Direct Sums of Unit-Endoregular Modules

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 r...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2018-11, Vol.61 (4), p.1103-1112
Main Authors: Zhang, Xiaoxiang, Lee, Gangyong
Format: Article
Language:English
Subjects:
Group theory
Modules
Rings (mathematics)
Sums
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Summary: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091518000135