$\displaystyle \delta$-Primary Elements In Lattice Modules

Abstract

In this paper, we introduce the expansion function $\delta$ on an $L$-module $M$. We define and investigate a $\delta$-primary element in an $L$-module $M$. Its characterizations and many of its properties are obtained. $\delta_0$-primary and $\delta_1$-primary elements of an $L$-module $M$ are related with 2-absorbing, 2-absorbing primary elements of an $L$-module $M$ to obtain their special properties. The element $\delta_1(N)\in M$ is related to $rad(N)\in M$, the radical element of $M$ to obtain its properties where $N\in M$. We define a $\delta_L$-primary element in an $L$-module $M$ where $\delta_L$ is an expansion function on $L$ and find relation among a $\delta_L$-primary element of $M$ and its corresponding $\delta_L$-primary element of $L$.