Том 71
№ 6

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Büyükaşık Е.

Articles: 1
Brief Communications (English)

Strongly radical supplemented modules

Büyükaşık Е., Türkmen E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1140-1146

Zoschinger studied modules whose radicals have supplements and called these modules radical supplemented. Motivated by this, we call a module strongly radical supplemented (briefly srs) if every submodule containing the radical has a supplement. We prove that every (finitely generated) left module is an srs-module if and only if the ring is left (semi)perfect. Over a local Dedekind domain, srs-modules and radical supplemented modules coincide. Over a no-local Dedekind domain, an srs-module is the sum of its torsion submodule and the radical submodule.