2021/09/20 by C. Matthew Evans, Evans, C. Matthew
Computer Science · #06E99 #06F35 #08A30 #Advanced Algebra and Logic #FOS: Mathematics #Logic, Reasoning, and Knowledge #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2109.09291
openalex publication_date 2021/09/20 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Given a complete atomic Boolean algebra, we show there is a commutative BCK-algebra whose ideal lattice is that Boolean algebra. This result is shown to exist within a larger framework involving BCK-algebras of functions, whose ideals and prime ideals are analyzed by way of a specific Galois connection. As a corollary of the main theorem, we show that every discrete topological space is the prime spectrum of a cBCK-algebra.