Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra

Autor:	Evans, C. Matthew
Rok vydání:	2021
Předmět:	Mathematics - Rings and Algebras 06F35 08A30 06E99
Druh dokumentu:	Working Paper
Popis:	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. Comment: Published in the European Journal of Mathematics (volume 10, June 2024)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.09291 Zobrazit plný text záznamu View this record from Arxiv