Multirelational representation theorems for complete idempotent left semirings

被引:0
|
作者
Furusawa, Hitoshi [1 ]
Nishizawa, Koki [2 ]
机构
[1] Kagoshima Univ, Dept Math & Comp Sci, Kagoshima 8900065, Japan
[2] Kanagawa Univ, Dept Informat Syst Creat, Kanagawa 2218686, Japan
基金
日本学术振兴会;
关键词
Complete idempotent left semirings; Multirelations; Representation theorem;
D O I
10.1016/j.jlamp.2014.08.008
中图分类号
TP301 [理论、方法];
学科分类号
081202 ;
摘要
Complete idempotent left semirings are a relaxation of quantales by giving up strictness and distributivity of composition over arbitrary joins from the left. It is known that the set of up-closed multirelations over a set forms a complete idempotent left semiring together with union, multirelational composition, the empty multirelation, and the membership relation. This paper provides a sufficient condition for a complete idempotent left semiring to be isomorphic to a complete idempotent left semiring consisting of up-closed multirelations, in which all joins, the least element, multiplication, and the unit element are respectively given by unions, empty multirelations, the multirelational composition, and the membership relation. Some equivalent conditions of the sufficient condition are also provided. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:426 / 439
页数:14
相关论文
共 50 条
  • [31] IDEMPOTENT DISTRIBUTIVE SEMIRINGS .2.
    PASTIJN, F
    SEMIGROUP FORUM, 1983, 26 (1-2) : 151 - 166
  • [32] On a variety of commutative multiplicatively idempotent semirings
    Ivan Chajda
    Helmut Länger
    Semigroup Forum, 2017, 94 : 610 - 617
  • [33] On simpleness of semirings and complete semirings
    Katsov, Yefim
    Tran Giang Nam
    Zumbraegel, Jens
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (06)
  • [34] Subdirectly irreducible commutative multiplicatively idempotent semirings
    Ivan Chajda
    Helmut Länger
    Algebra universalis, 2016, 76 : 327 - 337
  • [35] The variety of commutative additively and multiplicatively idempotent semirings
    Chajda, Ivan
    Laenger, Helmut
    SEMIGROUP FORUM, 2018, 96 (02) : 409 - 415
  • [36] Proper/Residually-Finite Idempotent Semirings
    Griffing, Gary
    SEMIGROUP FORUM, 2013, 86 (03) : 486 - 510
  • [37] Congruence-simple multiplicatively idempotent semirings
    Kepka, Tomas
    Korbelar, Miroslav
    Landsmann, Guenter
    ALGEBRA UNIVERSALIS, 2023, 84 (02)
  • [38] L-subvarieties of the variety of idempotent semirings
    Zhao, XZ
    Shum, KP
    Guo, YQ
    ALGEBRA UNIVERSALIS, 2001, 46 (1-2) : 75 - 96
  • [39] Proper/Residually-Finite Idempotent Semirings
    Gary Griffing
    Semigroup Forum, 2013, 86 : 486 - 510
  • [40] Structures of idempotent matrices over chain semirings
    Kanc, Kyung-Tae
    Song, Seok-Zun
    Yang, Younc-Oh
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2007, 44 (04) : 721 - 729