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• W2058095078 abstract "We prove that for a ring $R$, the following are equivalent: (i) Every right $R$-module is a direct sum of extending modules, and (ii) $R$ has finite type and right colocal type (i.e., every indecomposable right $R$-module has simple socle). Thus, in this case, $R$ is two-sided Artinian and right serial, and every right $R$-module is a direct sum of finitely generated uniform modules. This property of a ring is not left-right symmetric. A consequence is the following: $R$ is Artinian serial if and only if every $R$-module is a direct sum of extending modules if and only if $R$ is left serial with every right $R$-module a direct sum of extending modules." @default.
• W2058095078 created "2016-06-24" @default.
• W2058095078 creator A5065948680 @default.
• W2058095078 date "2009-01-30" @default.
• W2058095078 modified "2023-09-26" @default.
• W2058095078 title "Rings whose modules are direct sums of extending modules" @default.
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• W2058095078 doi "https://doi.org/10.1090/s0002-9939-09-09807-4" @default.
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