MODULES WHOSE PRIMARY-LIKE SUBMODULES ARE
INTERSECTION OF MAXIMAL SUBMODULES
Fatemeh Rashedi
Department of Mathematics
Technical and Vocational University (TVU) Tehran, IRAN

Abstract

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. A ring $R$ in which every prime ideal is an intersection of maximal ideals is called Hilbert (or Jacobson) ring. We propose to define modules by the property that primary-like submodules are intersections of maximal submodules which are said to be $\mathcal{PH} $ modules. It is shown that every co-semisimple module is a $\mathcal{PH} $ module. Also, it is shown that an $R$-module $M$ is a $\mathcal{PH} $ module if and only if every non-maximal primary-like submodule of $M$ is an intersection of properly larger primary-like submodules.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 6
Year: 2022

DOI: 10.12732/ijam.v35i6.5

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