2017
Том 69
№ 9

# Generalizations of $\oplus$-supplemented modules

Abstract

We introduce $\oplus$-radical supplemented modules and strongly $\oplus$-radical supplemented modules (briefly, $srs^{\oplus}$-modules) as proper generalizations of $\oplus$-supplemented modules. We prove that (1) a semilocal ring $R$ is left perfect if and only if every left $R$-module is an $\oplus$-radical supplemented module; (2) a commutative ring $R$ is an Artinian principal ideal ring if and only if every left $R$-module is a $srs^{\oplus}$-module; (3) over a local Dedekind domain, every $\oplus$-radical supplemented module is a $srs^{\oplus}$-module. Moreover, we completely determine the structure of these modules over local Dedekind domains.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 4, pp 612-622.

Citation Example: Pancar A., Türkmen B. N. Generalizations of $\oplus$-supplemented modules // Ukr. Mat. Zh. - 2013. - 65, № 4. - pp. 555-564.

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