Abstract: The notion of strong join-hyperlattices and the notions of hyperideals and hyperfilters in strong join-hyperlattices are introduced. The hyperideal generated by a∈L is studied and the distributivity of I(a∧b) is proved. Moreover, hyperlattices with condition “*” is discussed and the prime hyperfilter theorem of strong join-hyperlattices is also given.

Key words: strong join-hyperlattice, hyperideal, hyperfilter, prime hyperfilter