On quasi n-absorbing elements of multiplicative lattices

TL;DR

This paper introduces quasi n-absorbing elements in multiplicative lattices, exploring their properties and relationships with other types of absorbing elements to deepen the understanding of lattice structures.

Contribution

It defines and studies the properties of quasi n-absorbing elements, a novel concept in the theory of multiplicative lattices, and relates them to existing absorbing elements.

Findings

Established properties of quasi n-absorbing elements.

Derived relations between prime, 2-absorbing, and n-absorbing elements.

Enhanced the structural understanding of multiplicative lattices.

Abstract

In this study, we introduce the concept of quasi n-absorbing elements of multiplicative lattices. A proper element q is said to be a quasi n-absorbing element of L if whenever $a^nb\le q$ implies that either $a^n\le q$ or $a^{n-1}b\le q$. We investigate properties of this new type of elements and obtain some relations among prime, 2-absorbing, n-absorbing elements in multiplicative lattices.