Abstract: In this paper, we extend the concepts of primal and
weakly primal ideals for posets. Further, the diameter of the zero
divisor graph of a poset with respect to a non-primal ideal is
determined. The relation between primary and primal ideals in posets
is also studied.
Abstract: We introduced the notions of (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule as a generalization of prime ideal and jointly prime (R, S)-submodule, respectively. We provide a relationship between (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule. Characterizations of (1, k)-jointly prime (R, S)- submodules are also given.
Abstract: 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 semigroups. Furthermore, we introduce the notion of semiprime fuzzy ideals of ordered semigroup S and establish the relations between completely semiprime fuzzy ideals and semiprime fuzzy ideals of S. Finally, we give a characterization of prime fuzzy ideals of an ordered semigroup S and show that a nonconstant fuzzy ideal f of an ordered semigroup S is prime if and only if f is twovalued, and max{f(a), f(b)} = inf f((aSb]), ∀a, b ∈ S.
Abstract: The notion of intuitionistic fuzzy sets was introduced
by Atanassov as a generalization of the notion of fuzzy sets. Y.B. Jun
and S.Z. Song introduced the notion of intuitionistic fuzzy points.
In this paper we find some relations between the intuitionistic fuzzy
ideals of a semigroup S and the set of all intuitionistic fuzzy points
of S.