Abstract
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.
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