In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...

1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...

the minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of c(x). the necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) i is an intersection of o , s, when x is basically disconnected. (iii) i=o , when x x ha...

In this paper we have discussed the relations between Maximal ideal, Prime ideal and irreducible ideal in an incline R. Mathematics Subject Classification: 16D25, 16Y60