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.
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页码：635 / 636
页数：2
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