Orthomodular lattices as L-algebras

Yali Wu; Yichuan Yang

doi:10.1007/s00500-020-05242-7

Orthomodular lattices as L-algebras

Yali Wu
, Yichuan Yang^*

^*此作品的通讯作者

数学科学学院

Beihang University
Hebei GEO University

科研成果: 期刊稿件 › 文章 › 同行评审

20 引用（Scopus）

摘要

We first prove that the axioms system of orthomodular L-algebra (O-L-algebras for short) as given in [Rump: Forum Mathematicum, 30(4), 2018: 973–995] are not independent by giving an independent axiom one. Then, two conditions for KL-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure of OM-L-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.

源语言	英语
页（从-至）	14391-14400
页数	10
期刊	Soft Computing
卷	24
期	19
DOI	https://doi.org/10.1007/s00500-020-05242-7
出版状态	已出版 - 1 10月 2020

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author = "Yali Wu and Yichuan Yang",

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AU - Yang, Yichuan

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N2 - We first prove that the axioms system of orthomodular L-algebra (O-L-algebras for short) as given in [Rump: Forum Mathematicum, 30(4), 2018: 973–995] are not independent by giving an independent axiom one. Then, two conditions for KL-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure of OM-L-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.

AB - We first prove that the axioms system of orthomodular L-algebra (O-L-algebras for short) as given in [Rump: Forum Mathematicum, 30(4), 2018: 973–995] are not independent by giving an independent axiom one. Then, two conditions for KL-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure of OM-L-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.

KW - L-algebra

KW - OM-L-algebra

KW - Orthomodular lattice

KW - Self-similar closure

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VL - 24

SP - 14391

EP - 14400

JO - Soft Computing

JF - Soft Computing

IS - 19

ER -

Orthomodular lattices as L-algebras

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