New Results on Congruence Boolean Lifting Property
George Georgescu

TL;DR
This paper extends recent results on the Congruence Boolean Lifting Property ($CBLP$) from commutative rings to a broader class of algebraic structures, providing characterizations and conditions for $CBLP$ in congruence modular algebras.
Contribution
It generalizes the concept of $CBLP$ to semidegenerate congruence modular algebras and offers new characterization theorems and conditions for $CBLP$ applicability.
Findings
Characterization theorem for congruences with $CBLP$
Conditions ensuring $CBLP$ in various algebraic structures
Application of reticulation in analyzing $CBLP$
Abstract
The Lifting Idempotent Property () of ideals in commutative rings inspired the study of Boolean lifting properties in the context of other concrete algebraic structures (-algebras, commutative l-groups, -algebras, bounded distributive lattices, residuated lattices,etc.), as well as for some types of universal algebras (C. Muresan and the author defined and studied the Congruence Boolean Lifting Property () for congruence modular algebras). A lifting ideal of a ring is an ideal of fulfilling . In a recent paper, Tarizadeh and Sharma obtained new results on lifting ideals in commutative rings. The aim of this paper is to extend an important part of their results to congruences with in semidegenerate congruence modular algebras. The reticulation of such algebra will play an important role in our investigations (recall that the reticulation of a…
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory
