2-absorbing hyperideals and homomorphisms in join hyperlattices
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Keywords:prime hyperideal, Hyperlattice, radical
In this paper, we investigate hyperlattices, which arise by replacing one (or both) binary operation(s) of a lattice with hyperoperation(s). Several authors have studied prime generalizations of ideals in rings as well as lattices. We focus on the prime generalizations of hyperideals in join hyperlattices. Specifically, we introduce the concept of $2$-absorbing, primary $2$-absorbing primary etc.. in join hyperlattices and explore their interrelations. We establish that the intersection of two prime hyperideals is 2-absorbing, and the intersection of two $Q$-primary hyperideals is 2-absorbing primary. Additionally, we deal with the study of homomorphic images and pre-images of various types of hyperideals in join hyperlattices.
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