Filters of lattices with respect to a congruence
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 2
Abstract
Some properties of filters on a lattice L are studied with respect to a congruence on L. The notion of a θ-filter of L is introduced and these filters are then characterized in terms of classes of θ. For distributive L, an isomorphism between the lattice of θ-filters of L and the lattice of filters of L/θ is obtained. Keywords: congruence, filter, closure operator, θ-filter, congruence lattice. 2010 Mathematics Subject Classification: 06D99.
Authors and Affiliations
Abd El-Mohsen Badawy, M. Sambasiva Rao
Keywords
Related Articles
- EP ID EP165574
- DOI -
- Views 23
- Downloads 0
Left Zeroid and Right Zeroid Elements of Γ-Semirings
In this paper we introduce the notion of a left zeroid and a right zeroid of -semirings. We prove that, a left zeroid of a simple -semiring M is regular if and only if M is a regular -semiring.
WEAK-HYPERLATTICES DERIVED FROM FUZZY CONGRUENCES
In this paper we explore the connections between fuzzy congruence relations, fuzzy ideals and homomorphisms of hyperlattices. Indeed, we introduce the concept of fuzzy quotient set of hyperlattices as it was done in the...
DEVELOPED ZARISKI TOPOLOGY-GRAPH
In this paper, we introduce the developed Zariski topology-graph associated to an R-module M with respect to a subset X of the set of all quasi-prime submodules of M and investigate the relationship between the algebraic...
An ideal-based zero-divisor graph of direct products of commutative rings
In this paper, specifically, we look at the preservation of the diameter and girth of the zero-divisor graph with respect to an ideal of a commutative ring when extending to a finite direct product of commutative rings....
COMPLICATED BE-ALGEBRAS AND CHARACTERIZATIONS OF IDEALS
In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive a...