11 citations · 19 across the 12 of their papers we have counts for
16 papers
Reticulation of Quasi-commutative Algebras
George Georgescu
The commutator operation in a congruence-modular variety allows us to define the prime congruences of any algebra and the prime spectrum …
Reticulation functor and the transfer properties
George Georgescu
It is known that by using the commutator operation, for each congruence modular algebra one can define a notion of prime congruence. The set of prime congruences of $…
New Results on Congruence Boolean Lifting Property
George Georgescu
The Lifting Idempotent Property () of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (-…
Congruence Extensions in Congruence-modular Varieties
George Georgescu, Leonard Kwuida, Claudia Mureşan
We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences w.r.t. the term condition commut…
Flat topology on prime, maximal and minimal prime spectra of quantales
George Georgescu
Several topologies can be defined on the prime, the maximal and the minimal prime spectra of a commutative ring; among them, we mention the Zariski topology, the patch topology and…
Reticulation of a quantale, pure elements and new transfer properties
George Georgescu
We know from a previous paper that the reticulation of a coherent quantale is a bounded distributive lattice whose prime spectrum is homeomorphic to - prime spectrum…
Functorial Properties of the Reticulation of a Universal Algebra
George Georgescu, Leonard Kwuida, Claudia Mureşan
The {\em reticulation} of an algebra is a bounded distributive lattice whose prime spectrum of ideals (or filters), endowed with the Stone topology, is homeomorphic to the prim…
Boolean lifting property in quantales
Daniela Cheptea, George Georgescu
In ring theory, the lifting idempotent property (LIP) is related to some important classes of rings: clean rings, exchange rings, local and semilocal rings, Gelfand rings,maximal r…
The Reticulation of a Universal Algebra
George Georgescu, Claudia Mureşan
The reticulation of an algebra is a bounded distributive lattice whose prime spectrum of filters or ideals is homeomorphic to the prime spectrum of congruences of…
Going Up and Lying Over in Congruence--modular Algebras
George Georgescu, Claudia Mureşan
In this paper, we extend properties Going Up and Lying Over from ring theory to the general setting of congruence--modular equational classes, using the notion of prime congruence…
Factor Congruence Lifting Property
George Georgescu, Claudia Mureşan
In previous work, we have introduced and studied a lifting property in congruence--distributive universal algebras which we have defined based on the Boolean congruences of such al…
Congruence Boolean Lifting Property
George Georgescu, Claudia Mureşan
We introduce and study the Congruence Boolean Lifting Property (CBLP) for congruence--distributive universal algebras, as well as a property related to CBLP, which we have called $…
Algebraic and Topological Results on Lifting Properties in Residuated Lattices
Daniela Cheptea, George Georgescu, Claudia Mureşan
We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next w…
Boolean Lifting Property for Residuated Lattices
George Georgescu, Claudia Muresan
In this paper we define the Boolean Lifting Property (BLP) for residuated lattices to be the property that all Boolean elements can be lifted modulo every filter, and study residua…
Generalized Bosbach States
George Georgescu, Claudia Mureşan
Bosbach states represent a way of probabilisticly evaluating the formulas from various (commutative or non-commutative) many-valued logics. They are defined on the algebras corresp…
Maximal residuated lattices with lifting Boolean center
George Georgescu, Laurenţiu Leuştean, Claudia Mureşan
In this paper we define, inspired by ring theory, the class of maximal residuated lattices with lifting Boolean center and prove a structure theorem for them: any maximal residuate…