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Some results on quasi-t-dual Baer modules

Rachid TribakYahya TalebiMehrab Hosseinpour — 2023

Commentationes Mathematicae Universitatis Carolinae

Let R be a ring and let M be an R -module with S = End R ( M ) . Consider the preradical Z ¯ for the category of right R -modules Mod- R introduced by Y. Talebi and N. Vanaja in 2002 and defined by Z ¯ ( M ) = { U M : M / U is small in its injective hull } . The module M is called quasi-t-dual Baer if ϕ ϕ ( Z ¯ 2 ( M ) ) is a direct summand of M for every two-sided ideal of S , where Z ¯ 2 ( M ) = Z ¯ ( Z ¯ ( M ) ) . In this paper, we show that M is quasi-t-dual Baer if and only if Z ¯ 2 ( M ) is a direct summand of M and Z ¯ 2 ( M ) is a quasi-dual Baer module. It is also shown that any direct summand of a...

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