Neutrosophic primary submodule, localization and residual quotients

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran

2 Department of Computer Science, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran

Abstract

Let $R$ be a commutative ring with identity, $M$ be a unital $R$-module and let $L$ be a complete Heyting algebra. In this paper, among results on colon structures of $L$-neutrosophic submodules and $L$-neutrosophic ideals, we introduce and study the notion of primary (and prime) $L$-neutrosophic submodules and give connections with primary (prime) behavior of its $t$, $i$ and $f$ components. Then, for a multiplicatively closed subset $S$ of $R$, we define the notion of localization formation for an $L$-neutrosophic submodule $\lambda$ of $M$ and study its behavior. Some types of $L$-neutrosophic quotients will also be investigated.

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Journal of Algebra and Related Topics
Volume 12, Issue 2
January 2025
Pages 53-73

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