论文标题
CBCK-Elgebras的光谱特性
Spectral properties of cBCK-algebras
论文作者
论文摘要
在本文中，我们研究了交换性BCK-Elgebras的原始光谱。我们使用扎根的树提供了新的bck-Elgebras的结构，并确定了此类代数的理想晶格和主要理想晶格。我们证明，任何交换性BCK-Algebra的光谱是一个局部紧凑的广义光谱空间，并且仅当代数是有限地生成理想时的，并且仅当代数有限地生成时。此外，我们表明，如果交换性BCK-Algebra具有敬意，那么它的频谱就是Priestley空间。最后，我们考虑频谱的函数属性，并将函数定义为从交换性BCK-Algebras类别定义为零的分布晶格类别。我们对一个问题给出了部分答案：该函子的图像中有哪些分布晶格？
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?
