Homomorphisms and direct sum of uniserial modules

A right 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 characterize the finitely generated submodule N of a QTAG-module M such that all homomorphisms or monomorphisms of the finitely generated submodule N into the QTAG-module M, or all endomorphisms of the finitely generated submodule N, extends to an endomorphism of the QTAG-module M.

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Keywords

Ulm sequences, QTAG-modules, valuation

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