ON (m, n)−ABSORBING IDEALS IN AN ADL
On (m, n)−AIs
Keywords:
Almost Distributive Lattice (ADL); (m, n)−absorbing ideal; Weakly (m, n) −absorbing ideal; (m, n)−absorbing prime ideal; weakly (m, n)−absorbing prime ideal.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.
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