Commutative bounded integral residuated orthomodular lattices are Boolean algebras

被引：0
作者：
Tkadlec, Josef [1 ]
Turunen, Esko [2 ]
机构：
[1] Czech Tech Univ, Prague 16627, Czech Republic
[2] Tampere Univ Technol, FIN-33101 Tampere, Finland
来源：
SOFT COMPUTING | 2011年 / 15卷 / 04期
关键词：
Residuated lattice; Orthomodular lattice;
D O I：
10.1007/s00500-010-0572-4
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We show that a commutative bounded integral orthomodular lattice is residuated iff it is a Boolean algebra. This result is a consequence of (Ward, Dilworth in Trans Am Math Soc 45, 336-354, 1939, Theorem 7.31); however, out proof is independent and uses other instruments.
引用
收藏
页码：635 / 636
页数：2
相关论文
共 50 条
  • [21] ORTHOMODULAR LATTICES CAN BE CONVERTED INTO LEFT RESIDUATED L-GROUPOIDS
    Chajda, Ivan
    Laenger, Helmut
    MISKOLC MATHEMATICAL NOTES, 2017, 18 (02) : 685 - 689
  • [22] Residuated lattices and lattice effect algebras
    Zhou, Xiang-Nan
    Li, Qing-Guo
    Wang, Guo-Jun
    FUZZY SETS AND SYSTEMS, 2007, 158 (08) : 904 - 914
  • [23] On the Structure of Finite Integral Commutative Residuated Chains
    Horcik, Rostislav
    JOURNAL OF LOGIC AND COMPUTATION, 2011, 21 (05) : 717 - 728
  • [24] The subvariety lattice for representable idempotent commutative residuated lattices
    Jeffrey S. Olson
    Algebra universalis, 2012, 67 : 43 - 58
  • [25] On Non-commutative Residuated Lattices With Internal States
    Zhao, Bin
    He, Pengfei
    IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2018, 26 (03) : 1387 - 1400
  • [26] Archimedean classes in integral commutative residuated chains
    Horcik, Rostislav
    Montagna, Franco
    MATHEMATICAL LOGIC QUARTERLY, 2009, 55 (03) : 320 - 336
  • [27] Interior and closure operators on bounded residuated lattices
    Rachunek, Jiri
    Svoboda, Zdenek
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2014, 12 (03): : 534 - 544
  • [28] Rough approximations in non-commutative residuated lattices
    Bakhshi M.
    Izanlou M.
    Afrika Matematika, 2018, 29 (1-2) : 97 - 114
  • [29] Local bounded commutative residuated l-monoids
    Rachunek, Jiri
    Salounova, Dana
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2007, 57 (01) : 395 - 406
  • [30] Boolean filters and positive implicative filters of residuated lattices
    Lianzhen, Liu
    Kaltai, Li
    INFORMATION SCIENCES, 2007, 177 (24) : 5725 - 5738
12345