cBCK-代数的谱性质

IF 0.6 4区 数学 Q3 MATHEMATICS
C. Matthew Evans
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引用次数: 2

摘要

本文研究了交换BCK-代数的素数谱。我们利用根树给出了交换BCK-代数的一个新构造,并确定了这类代数的理想格和素理想格。我们证明了任何交换BCK代数的谱是一个局部紧致的广义谱空间,它是紧致的当且仅当该代数是有限生成的理想。此外,我们证明了如果交换BCK代数是对合的,那么它的谱是Priestley空间。最后,我们考虑了谱的函子性质,并定义了一个从交换BCK-代数范畴到零分配格范畴的函子。我们给出了这个问题的部分答案:这个函子的图像中有什么分配格?
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Spectral properties of cBCK-algebras

Spectral properties of cBCK-algebras

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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来源期刊
Algebra Universalis
Algebra Universalis 数学-数学
CiteScore
1.00
自引率
16.70%
发文量
34
审稿时长
3 months
期刊介绍: Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
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