2019
Том 71
№ 2

# On strongly $\oplus$-supplemented modules

Abstract

In this work, strongly $\oplus$-supplemented and strongly cofinitely $\oplus$-supplemented modules are defined and some properties of strongly $\oplus$-supplemented and strongly cofinitely $\oplus$-supplemented modules are investigated. Let $R$ be a ring. Then every $R$-module is strongly $\oplus$-supplemented if and only if R is perfect. Finite direct sum of $\oplus$-supplemented modules is $\oplus$-supplemented. But this is not true for strongly $\oplus$-supplemented modules. Any direct sum of cofinitely $\oplus$-supplemented modules is cofinitely $\oplus$-supplemented but this is not true for strongly cofinitely $\oplus$-supplemented modules. We also prove that a supplemented module is strongly $\oplus$-supplemented if and only if every supplement submodule lies above a direct summand.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 5, pp 768-775.

Citation Example: Nebiyev C., Pancar A. On strongly $\oplus$-supplemented modules // Ukr. Mat. Zh. - 2011. - 63, № 5. - pp. 662-667.

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