Tayyabeh Amouzegar, Ali Reza Moniri Hamzekolaee, Adnan Tercan: Fully invariant submodules for constructing dual Rickart modules and dual Baer modules, 295-306

Abstract:

Fully invariant submodules play an important designation in studying the structure of some known modules such as (dual) Rickart and (dual) Baer modules. In this work, we introduce $F$-dual Rickart (Baer) modules via the concept of fully invariant submodules. It is shown that $M$ is $F$-dual Rickart if and only if $M=F\oplus L$ such that $F$ is a dual Rickart module. We prove that a module $M$ is $F$-dual Baer if and only if $M$ is $F$-dual Rickart and $M$ has $SSSP$ for direct summands of $M$ contained in $F$. We present a characterization of right $I$-dual Baer rings where $I$ is an ideal of $R$. Some counter-examples are provided to illustrate new concepts.

Key Words: Fully invariant submodule, dual Rickart module, $F$-dual Rickart module, $F$-dual Baer module.

2010 Mathematics Subject Classification: Primary 16D10; Secondary 16D80.

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