On projection-invariant submodules of QTAG-modules | Zendy

Fahad Sikander | Zendy; Alveera Mehdi | Zendy; Sabah A. R. K. Naji | Zendy

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On projection-invariant submodules of QTAG-modules

Author(s) -

Fahad Sikander,

Alveera Mehdi,

Sabah A. R. K. Naji

Publication year - 2015

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.1016/j.joems.2015.01.005

Subject(s) - mathematics , invariant (physics) , projection (relational algebra) , pure mathematics , arithmetic , algorithm , mathematical physics

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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