Strongly radical supplemented modules
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...
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| Date: | 2011 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2792 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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