Coatomic refinable modules

Year 2020, Volume: 2 Issue: 2, 92 - 97, 26.08.2020

Burcu Nişancı Türkmen , Ergül Türkmen

https://doi.org/10.38058/ijsl.774962

Abstract

In this article, we define the concept of (strongly) coatomic refinable modules as a proper generalization of (strongly) refinable modules. It is shown that: (1) every direct summand of a coatomic refinable module is coatomic refinable; (2) over a left max ring a module M is (strongly) coatomic refinable if and only if it is (strongly) refinable; (3) if a coatomic refinable module M is π-projective, then it is strongly coatomic refinable; (4) if coatomic direct summands lift modulo every coatomic submodule of M, then M is coatomic refinable.

Keywords

refinable module, coatomic module, coatomic refinable module

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