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arXiv · 2109.09291

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

C. Matthew Evans
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Abstract

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.

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C. Matthew Evans. 2021-09-20. Every complete atomic Boolean algebra is the ideal lattice of a cBCK-algebra. https://arxiv.org/abs/2109.09291

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