量子B-代数的可逆元

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英文篇名：On the Invertible Elements of Quantum B-Algebras 作者：顾晓娟 ; 韩胜伟 英文作者：GU Xiaojuan;HAN Shengwei;School of Mathematics and Information Science,Shaanxi Normal University; 关键词：Quantale ; 量子B-代数 ; 偏序群 ; 可逆元 英文关键词：quantale;;quantum B-algebras;;partially ordered group;;invertible element 中文刊名：SCSD 英文刊名：Journal of Sichuan Normal University(Natural Science) 机构：陕西师范大学数学与信息科学学院; 出版日期：2019-05-20 出版单位：四川师范大学学报(自然科学版) 年：2019 期：v.42 基金：国家自然科学基金(11531009) 语种：中文; 页：SCSD201903004 页数：4 CN：03 ISSN：51-1295/N 分类号：28-31

摘要

量子B-代数是一种非可换的逻辑代数,它可以看作是Quantale的一种推广.量子B-代数包含了多种蕴含代数,其中偏序群就是一种特殊的量子B-代数.主要研究了量子B-代数的可逆元,证明了所有可逆元构成一个偏序群.
        Quantum B-algebras are a class of non-commutative logical algebras,which can be seen as a generalization of quantales.Quantum B-algebras cover a majority of implication algebras such as partially ordered groups which are a special class of quantum B-algebras. In this paper,the invertible elements of quantum B-algebras are investigated,and it is shown that the set of all invertible elements of quantum B-algebras is a partially ordered group.

引文

[1]RUMP W. Quantum B-algebras[J]. Central European J Math,2013,11(11):1881-1899.
    [2]RUMP W,YANG Y C. Non-commutative logical algebras and algebraic quantales[J]. Ann Pure Appl Logic,2014,165(2):759-785.
    [3]RUMP W. The completion of quantum B-algebras[J]. Cahiers Top Geom Diff Categ,2016,53(3):203-228.
    [4]RUMP W. Quantum B-algebras:their omnipresence in algebraic logic and beyond[J]. Soft Comput,2017,21(10):2521-2529.
    [5]HAN S W,XU X T,QIN F. The unitality of quantum B-algebras[J]. Inter J Theor Phys,2018,57(5):1582-1590.
    [6]BIRKHOFF G. Lattice Theory[M]. Providence RI:Am Math Soc,1940.
    [7]韩胜伟,赵彬. Quantale理论基础[M].北京:科学出版社,2016.