University of Guilan Journal of Algebra and Related Topics 2345-3931 12 2 2025 01 01 Neutrosophic primary submodule, localization and residual quotients 53 73 8325 10.22124/jart.2024.24631.1532 EN S. Azimi Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran N. Zamani Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran M. R. Hooshmandasl Department of Computer Science, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran A. Khojali Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, Ardabil, Iran Journal Article 2023 05 31 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. https://jart.guilan.ac.ir/article_8325_3b9bc72959f56330322fa435ebd67bac.pdf