In this paper we study the prime ideals space of a BL-algebra, proved that the prime ideals space being a 0 T-space and also a stone space. Furthermore, we study the properties of the prime ideals space.

For standard graded Artinian K-algebras defined by componentwise linear ideals and Gotzmann ideals, we give conditions for the weak Lefschetz property in terms of numerical invariants of the defining ideals.

The notions of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are introduced, and related properties are investigated. Characterizations of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are discussed. A regular semigroup is characterized by the notion of a uni-soft quasi ideal.

We study cyclic codes of length pk over GR(p2,m), or equivalently, ideals of the ring GR(p2,m)/ 〈upk − 1〉. We derive a method of representing the ideals, and classify all ideals in the ring GR(p2,m)/ 〈upk − 1〉. We also analyse the duals, and identify the self-dual ideals. © 2008 Elsevier Inc. All rights reserved.

The aim of this paper is to introduce the concepts of fuzzy strong h-ideals and fuzzy congruences of hemirings. The quotient hemirings via fuzzy strong h-ideals are investigated. The relationships between fuzzy congruences and fuzzy strong h-ideals of hemirings are discussed. Pay attention to an open question on fuzzy congruences. Finally, the normal fuzzy strong h-ideals of hemirings are explo...

In this paper we introduce the notions of pure ideals, weakly pure ideals in ternary semigroups. We also de ne purely prime ideals of a ternary semigroup and study some properties of these ideals. The space of purely prime two-sided ideal is topologized.

The aim of this paper is to apply the concept of interval-valued intuitionistic fuzzy set to implicative ideals and commutative ideals in BCK-algebras and introduced the new notion of interval-valued intuitionistic fuzzy implicative ideals in BCK-algebras and interval-valued intuitionistic fuzzy commutative ideals in BCK-algebras and related properties are investigated.

In this paper, we introduce the concepts of fuzzy ideals, fuzzy implicative ideals and fuzzy p-ideals in BF-algebras and investigate some of its properties.

1. Let F be a partially ordered vector space with an order unit e. It is well known that the class 5DÎ of maximal ideals of V is in one-one correspondence with the class K of normalized positive linear functionals, in the sense that to each ME^SR corresponds a positive linear functional <¡>m with M as its null-space and with M(e) = 1. A maximal ideal MG 90? is said to be extreme if <pM is an...