-isomorphisms of distributive lattices
Weak Boolean products of bounded dually residuated -monoids
In the paper we deal with weak Boolean products of bounded dually residuated -monoids (DR-monoids). Since bounded DRl-monoids are a generalization of pseudo MV-algebras and pseudo BL-algebras, the results can be immediately applied to these algebras.
Weak homogeneity and Pierce’s theorem for -algebras
In this paper we prove a theorem on weak homogeneity of -algebras which generalizes a known result on weak homogeneity of Boolean algebras. Further, we consider a homogeneity condition for -algebras which is defined by means of an increasing cardinal property.
Weak homomorphisms of distributive p-algebras
Weak pseudo-complementations on ADL’s
The notion of an Almost Distributive Lattice (abbreviated as ADL) was introduced by U. M. Swamy and G. C. Rao [6] as a common abstraction of several lattice theoretic and ring theoretic generalization of Boolean algebras and Boolean rings. In this paper, we introduce the concept of weak pseudo-complementation on ADL’s and discuss several properties of this.
Weakly projectable and projectable W-algebras.
In this paper we introduce and study the weakly projectable and projectable W-algebras and we review the Representation Theorem of [1].
Weakly regular lattices
Weil nearness spaces.
Weil uniformities for frames
In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is expressed...
When doL-fuzzy ideals of a ring generate a distributive lattice?
The notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended...
When spectra of lattices of -ideals are Stone-Čech compactifications
Let be a completely regular Hausdorff space and, as usual, let denote the ring of real-valued continuous functions on . The lattice of -ideals of has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) precisely when is a -space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a -ideal if whenever two elements have the same annihilator and...