ON (m, n)−ABSORBING IDEALS IN AN ALMOST DISTRIBUTIVE LATTICE

Abstract

This paper explores the concept of (m, n)−absorbing ideals within an Almost Distributive Lattice (ADL). It also introduces and examines the notion of weakly (m, n)−absorbing ideals, a more generalized form of (m, n)− absorbing ideals. The primary focus is on establishing the relationships between (m, n)−absorbing ideals (and weakly (m, n)−absorbing ideals) and their counterparts, (m, n)−absorbing prime ideals (and weakly (m, n)−absorbing prime ideals), in an ADL. Additionally, the paper investigates the properties of homomorphic images and inverse images of (m, n)−absorbing ideals, demonstrating that these images retain the structure of (m, n)−absorbing ideals.