2021/10/10 by Katarzyna Słomczyńska, Słomczyńska, Katarzyna
Computer Science · Decision Sciences · #03B20 #03G25 #08B10 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO) #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2110.08040
openalex publication_date 2021/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A strongly Fregean algebra is an algebra such that the class of its homomorphic images is Fregean and the variety generated by this algebra is congruence modular. To understand the structure of these algebras we study the prime intervals projectivity relation in the posets of their completely meet irreducible congruences and show that its cosets have natural structure of Boolean group. In particular, this approach allows us to represent congruences and elements of such algebras as the subsets of upward closed subsets of these posets with some special properties.