Characterizations and Direct Sums of Unit-Endoregular Modules

Autor:	Gangyong Lee, Xiaoxiang Zhang
Rok vydání:	2018
Předmět:	Regular ring Pure mathematics Class (set theory) General Mathematics Baer ring Abelian group Characterization (mathematics) Indecomposable module Unit (ring theory) Endomorphism ring Mathematics
Zdroj:	Proceedings of the Edinburgh Mathematical Society. 61:1103-1112
ISSN:	1464-3839 0013-0915
DOI:	10.1017/s0013091518000135
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e01dc5e5bb4abea962c1b60c3e5f6f8d https://doi.org/10.1017/s0013091518000135 Zobrazit plný text záznamu