On the Socles of Commutator Invariant Submodules of $QTAG$-Modules

  • Ayazul Hasan Department of Mathematics Faculty of Science, Jazan University
Keywords: $QTAG$-modules, commutator invariant submodules, socles, commutator socle-regular $QTAG$-modules

Abstract

In [9, 8, 10], respectively, socles have been studied with the aid of fully invariant, characteristic and projection invariant submodules of $QTAG$-modules. Here we focus our attention on the socles of commutator invariant submodules and introduce a new class of modules, which we term commutator socle-regular $QTAG$-modules. After establishing some crucial properties of commutator socle-regularity, we show that the addition of separable summand to a module does not influence commutator socle-regularity.

Published
2018-08-22
How to Cite
Hasan, A. (2018). On the Socles of Commutator Invariant Submodules of $QTAG$-Modules. Armenian Journal of Mathematics, 10(7), 1-11. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/216