PS-Hollow Representations of Modules over Commutative Rings

Jawad Abuhlail; Hamza Hroub

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arXiv · 1804.06968

PS-Hollow Representations of Modules over Commutative Rings

Jawad Abuhlail·Hamza Hroub

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Abstract

Let $R$ be a commutative ring and $M$ a non-zero $R$-module. We introduce the class of \emph{pseudo strongly hollow submodules} (\emph{PS-hollow submodules}, for short) of $M$. Inspired by the theory of modules with \emph{secondary representations}, we investigate modules which can be written as \emph{finite} sums of PS-hollow submodules. In particular, we provide existence and uniqueness theorems for the existence of \emph{minimal} PS-hollow strongly representations of modules over Artinian rings.

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BibTeX RIS

Jawad Abuhlail, Hamza Hroub. 2019-07-31. PS-Hollow Representations of Modules over Commutative Rings. https://arxiv.org/abs/1804.06968

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