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

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 $N\in M$\mathrm{.}Wedefinea$\delta_L$-primaryelementinan$L$-module$M$where$\delta_L$isanexpansionfunctionon$L$andfindrelationamonga$\delta_L$-primaryelementof$M$anditscorresponding$\delta_L$-primary element of $L$.