f-Primary Ideals in Semigroups

Abstract

Right now, the terms left f-Primary Ideal, right f-Primary Idealand f- primary ideals are presented. It is Shown that An ideal U in a semigroup S fulfills the  condition that If G, H are two ideals of S with the end goal that f (G) f (H)⊆U and f(H)⊈U then f(G)⊆r_f (U)iff  f (q), f (r)⊆S , <f (q)><f (r)>⊆U and f (r)⊈U then  f (q)⊆r_f (U) in like manner it is exhibited that An ideal U out of a semigroup S fulfills condition If G, H are two ideals of S such that f (G) f (H)⊆U and f (G)⊈U then f (H) ⊆r_f (U) iff  f (q), f (r)⊆S,<f (q)><f (r)>⊆U and f (q)⊈U⇒f (r)⊆r_f (U). By utilizing the meanings of left - f- primary and right f- primary ideals a couple of conditions are illustrated It is shown that J is a restrictive maximal ideal in Son the off chance thatr_f (U) = J for some ideal U in S at that point J will be a f- primary ideal and Jⁿ is f-primary ideal for some n it is explained that if S is quasi-commutative then an ideal U of S is left f - primary iff right f -primary.