2-absorbing hyperideals and homomorphisms in join hyperlattices

In this paper, we investigate hyperlattices, which arise by replacing one (or both) binary operation(s) in a lattice with hyperoperation(s). Many authors have studied prime generalizations of ideals in rings and lattices. In this paper we focus on the prime generalizations of hyperideals in join hyper-lattices. We introduce the notions of 2-absorbing, primary 2-absorbing primary, etc., in join hyperlat-tices 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. Finally, we study the of homomorphic images and pre-images of various types of hyperideals in join hyperlattices.