Abstract

In this research we concentrate on the analytical study and concept of fuzzification on prime bi-ideals in ternary semigroups and look for some of their related characteristics. Strongly prime and semiprime fuzzy bi-ideals are initiated and traits are discussed. Besides irreducible and strongly irreducible fuzzy bi-ideals in ternary semigroups have been researched. Employing the fuzzy bi-ideals of ternary semigroups, parity statements for a regular ternary semigroup have been collaborated. Furthermore, it has observed that, the set of all strongly prime proper fuzzy bi-ideals in a ternary semigroup form a topology. Conclusively, it has been proved that in case of the totally ordered set of fuzzy bi-ideals of a semigroup $S$, the concept of irreducible prime and strongly irreducible prime coincides.

Keywords: Prime bi-ideals; strongly prime bi-ideals; semiprime bi-ideals; irreducible bi-ideals; ternary semigroups.

MSC: 20N10, 20N25, 20M12

Pages:  79$-$96     

Volume  64 ,  Issue  2 ,  2012