Completely Prime Fuzzy,Prime Fuzzy Ideal Of A Po Ternary Semigroup
Journal Title: International Journal of engineering Research and Applications - Year 2018, Vol 8, Issue 8
Abstract
In this Paper the terms [f), fuzzy left(right,lateral) identity, fuzzy left(right,lateral) zero of a po ternarysemigroup are introduced. It is proved that fuzzy left identity and fuzzy right identity and lateral zero of a poternary semigroup if it exists then they are same. And proved that fuzzy left zero ,fuzzy lateral zero ,fuzzy right zero of a po ternarysemigroup exists then they are equal.also proved that intersection of arbitrary family of fuzzy po ternary subsemigroups of a po ternary semigroup T is a fuzzy poternary subsemigroup of T. Furthermore, proved that intersection of all fuzzy po ternary semigroups of T containing f is ideal generated by fuzzy subset f. and also proved that f is a fuzzy ideal of a po ternary semigroup T ifffoToT⊆ f, ToTof⊆ f, TofoT⊆ f and f ⊆ f.And proved the union, intersection of arbitrary family of fuzzy ideals of po ternary semigroup T is fuzzy ideal of T.further proved that every completely prime fuzzy ideal is weakly completely prime fuzzy ideal. Also proved that if f is completely prime fuzzy ideal then ft is ternary sub semigroup and completely prime ideal of T. also proved that ft is completely prime ideal of T then f is weakly completely prime fuzzy and completely prime fuzzy ideal of T and proved that equivalent conditions of prime fuzzy ideal, f is prime fuzzy ideal iff 1-f is a fuzzy m-system ofT if 1− f ≠ ∅. Finally proved that every maximal fuzzy ideal of T is a prime fuzzy ideal of T. Mathematical subject classification (2010): 20M07; 20M11, 20M12
Authors and Affiliations
J. M. Pradeep, A. Gangadhara Rao, P. Ramyalatha, L. Achala
Keywords
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