Strongly t-continuous and Strongly t-semisimple Modules - Dakhil Shyaa , Farhan; Mohammed Ali Hadi, Inaam (Al-Qadisiyah Journal of Pure Science, 2019)
We introduce and investigate strongly t-continuous modules. A module is called strongly t-continuous if is strongly t-extending, and every submodule of which contains and is isomorphic to a direct summand is a fully invariant direct summand of . 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. is strongly t-continuous if and only if is strongly t-extending and the endomorphism ring of is Von Neumann regular, if and only if , where 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.