Functorial Properties of the Reticulation of a Universal Algebra

Georgescu, George; Kwuida, Léonard; Mureşan, Claudia (2021). Functorial Properties of the Reticulation of a Universal Algebra Journal of Applied Logics - IfCoLog Journal, 8(5), pp. 1124-1167.

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The reticulation of an algebra A is a bounded distributive lattice whose prime spectrum of ideals (or filters), endowed with the Stone topology, is homeomorphic to the prime spectrum of congruences of A, with its own Stone topology. The reticulation allows algebraic and topological properties to be transferred between the algebra A and this bounded distributive lattice, a transfer which is facilitated if we can define a reticulation functor from a variety containing A to the variety of (bounded) distributive lattices. In this paper, we continue the study of the reticulation of a universal algebra initiated in [27], where we have used the notion of prime congruence introduced through the term condition commutator, for the purpose of creating a common setting for the study of the reticulation, applicable both to classical algebraic structures and to the algebras of logics. We characterize morphisms which admit an image through the

Item Type:	Journal Article (Original Article)
Division/Institute:	Business School > Business Foundations and Methods Business School
Name:	Georgescu, George; Kwuida, Léonard0000-0002-9811-0747 and Mureşan, Claudia
ISSN:	2631-9829
Language:	English
Submitter:	Léonard Kwuida
Date Deposited:	27 Jul 2021 13:26
Last Modified:	13 Nov 2023 14:57
ARBOR DOI:	10.24451/arbor.15214
URI:	https://arbor.bfh.ch/id/eprint/15214