Strongly t-continuous and strongly t-semisimple modules

Abstract EN

We introduce and investigate strongly t-continuous modules.

A module ܯ is called strongly t-continuous if ܯ is strongly t-extending, and every submodule of ܯ which contains ܼଶ (ܯ (and is isomorphic to a direct summand is a fully invariant direct summand of ܯ .It is shown that, while a direct summand of strongly t-continuous inherits the property, a direct sum of strongly t-continuous modules don’t.

ܯ is strongly t-continuous if and only if ܯ is strongly t-extending and the endomorphism ring of ெ ௓మ (ெ) is Von Neumann regular, if and only if ܯܼ = ଶ ᇱܯ⨁(ܯ) , where ܯᇱ is a strongly t-continuous module.

We have shown that strongly t-continuous module and t-continuous module are coinciding under certain conditions.

Many other properties and example are given.