2017
Том 69
№ 7

All Issues

Strongly radical supplemented modules

Büyükaşık Е., Türkmen E.

Full text (.pdf)


Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 8, pp 1306-1313.

Citation Example: Büyükaşık Е., Türkmen E. Strongly radical supplemented modules // Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1140-1146.

Full text