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SpringerOpen, Journal of the Egyptian Mathematical Society, 2(24), p. 156-159, 2016

DOI: 10.1016/j.joems.2015.01.005

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On projection-invariant submodules of QTAG-modules

Journal article published in 2015 by Fahad Sikander, Alveera Mehdi, Sabah A. R. K. Naji
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

A module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules. Here we study projection-invariant submodule of QTAG-module. A submodule N of a QTAG-module M is said to be projection-invariant in M if f(N)⊆N, for all idempotent endomorphisms f in End(M). Clearly, fully invariant submodules are projection-invariant. Mehdi et. al. characterized fully invariant submodules and characteristic submodules with the help of their socles. Here we investigate the socles of projection-invariant submodules of QTAG-modules.