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Accessible Unlicensed Requires Authentication Published by De Gruyter January 19, 2016

On generalized submodules of QTAG-modules

Ayazul Hasan

Abstract

If α denotes the class of all QTAG-modules M such that M/Hβ(M) is totally projective for every ordinal β<α, then these modules are called α-modules. Here we study the relation between the structure of fully invariant submodules of certain QTAG-modules and the structure of containing modules. It is found that if F is a fully invariant submodule of the totally projective QTAG-module M, then both F and M/F are totally projective. We show that if for some sequence β=(βk)k<ω, both Mβ and M/Mβ are totally projective, then M itself is necessarily totally projective.

MSC: 16K20

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Received: 2014-5-4
Revised: 2015-7-15
Accepted: 2015-10-16
Published Online: 2016-1-19
Published in Print: 2016-6-1

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