Computation of prime hyperideals in meet hyperlattices

We define the concept of 2-absorbing hyperideal in a strong meet hyperlattice denoted by L, as a generalization of 2-absorbing ideal in a classical lattice. We compute the hyperideals those are, viz. 2-absorbing but not prime; primary but not prime; weakly 2-absorbing primary but not weakly primary, etc., which indicates that all these classes are different and generalize the respective notions of a classical lattice. We prove several properties of 2-absorbing hyperideals and annihilator hyper-ideals in L. Furthermore, we interrelate with the weakly κ hyperideals, where κ ∈ {prime, 2-absorbing, primary, 2-absorbing primary}, which proves that all these notions are completely determined as indicated in Figure 8. Also, we prove the homomorphism results on strong meet hyperlattices.