LEFT REGULAR AND INTRA-REGULAR ORDERED HYPERSEMIGROUPS IN TERMS OF SEMIPRIME AND FUZZY SEMIPRIME SUBSETS

Abstract

We prove that an ordered hypersemigroup H is left (resp. right) regular if and only if every left (resp. right) ideal of H is semiprime and it is intra-regular if and only if every ideal of H is semiprime. Then we prove that an ordered hypersemigroup H is left (resp. right) regular if and only if every fuzzy left (resp. right) ideal of H is fuzzy semiprime and it is intra-regular if and only if every fuzzy ideal of H is fuzzy semiprime.