Neutrosophic primary submodule, localization and residual quotients

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.