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ON DIFFERENT NOTIONS OF TRANSITIVITY FOR QTAG-MODULES

Sikander, Fahad;Hasan, Ayazul;Mehdi, Alveera

  • Received : 2015.05.25
  • Accepted : 2016.04.11
  • Published : 2016.06.25

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. Recently, the authors introduced the classes of QTAG-modules namely as socle-regular and strongly socle-regular QTAG-modules which properly contain the classes of transitive and fully transitive QTAG-modules respectively. Here we define strongly and quasi transitivities and study the inter relations between various type of transitivities.

Keywords

QTAG-module;Strongly;fully and weakly transitive module

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