On Generalization of $\delta$-Primary Elements in Multiplicative Lattices

Abstract

In this paper, we introduce $\varphi$-$\delta$-primary elements in a compactly generated multiplicative lattice $L$ and obtain its characterizations. We prove many of its properties and investigate the relations between these structures. By a counter example, it is shown that a $\varphi$-$\delta$-primary element of $L$ need not be $\delta$-primary and found conditions under which a $\varphi$-$\delta$-primary element of $L$ is $\delta$-primary.

14 pages, 3 figures