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Spectral properties of cBCK-algebras

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Abstract

In this paper we study prime spectra of commutative BCK-algebras. We give a new construction for commutative BCK-algebras using rooted trees, and determine both the ideal lattice and prime ideal lattice of such algebras. We prove that the spectrum of any commutative BCK-algebra is a locally compact generalized spectral space which is compact if and only if the algebra is finitely generated as an ideal. Further, we show that if a commutative BCK-algebra is involutory, then its spectrum is a Priestley space. Finally, we consider the functorial properties of the spectrum and define a functor from the category of commutative BCK-algebras to the category of distributive lattices with zero. We give a partial answer to the question: what distributive lattices lie in the image of this functor?

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  1. Mathematics Department, Oberlin College, Oberlin, OH,  44074, USA

    C. Matthew Evans

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  1. C. Matthew Evans
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Evans, C.M. Spectral properties of cBCK-algebras. Algebra Univers. 83, 25 (2022). https://doi.org/10.1007/s00012-022-00779-0

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