Multiplicative lattices with absorbing factorization

TL;DR

This paper explores the structure of multiplicative lattices by introducing and analyzing concepts of 1-absorbing prime elements and their factorizations, extending ideas from ring theory to lattice theory.

Contribution

It defines and studies OAFLs and TAFLs, new classes of C-lattices characterized by finite products of 1-absorbing prime elements and 2-absorbing factorizations.

Findings

Characterization of OAFLs and TAFLs.

Conditions under which elements factor into 1-absorbing primes.

Extension of prime ideal concepts from rings to lattices.

Abstract

In [24], Yassine et al. introduced the notion of 1-absorbing prime ideals in commutative rings with nonzero identity. In this article, we examine the concept of 1-absorbing prime elements in C-lattices. We investigate the C-lattices in which every element is a finite product of 1-absorbing prime elements (we denote them as OAFLs for short). Moreover, we study C-lattices having 2-absorbing factorization (we denote them as TAFLs for short).