A Note on the Axioms of Lattice Implication Algebra

Chinese Quarterly Journal of Mathematics ›› 2002, Vol. 16 ›› Issue (2): 71-76.

A Note on the Axioms of Lattice Implication Algebra

唐山师范学院数学系西南交通大学应用数学系西南交通大学应用数学系河北唐山063000四川成都610031

Received:2001-10-24 Online:2002-06-30 Published:2024-05-09
About author:ZHAO Guang-feng（1964－）,male,native of Taian,Shandong,Ph．D．,an associate professor of Tangshan Teacher’s College,engages in topology and intellagent control．
Supported by:
Supported by the National Natural Science Foundation of China（60074014）

Abstract

Abstract: 设在一个非空集合L上有一个二元运算和两个零元运算O与I ,除此之外没有其它已知的代数结构。利用这三个运算可以在L上定义一个一元运算′和两个二元运算∨和 ∧ (定义 2 .1 )。本文证明了只要这些运算满足格蕴涵代数的公理 (不包括有余格的公理 ) ,(L ,∨ ,∧ ,′)就是一个有泛界O ,I的有余格 (定理 2 .2 )。因此在定义格蕴涵代数时可以在一个没有任何代数结构的非空集合上定义蕴含运算而不必在一个有泛界的有余格上定义蕴含运算 ,而且在这两种定义方式中蕴含运算所满足的条件是相同的。

Key words: 格蕴涵代数, 格蕴涵代数公理, ,

CLC Number:

O153.1

ZHAO Guang-feng, XU Yang, SONG Zhen-ming. A Note on the Axioms of Lattice Implication Algebra[J]. Chinese Quarterly Journal of Mathematics, 2002, 16(2): 71-76.

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A Note on the Axioms of Lattice Implication Algebra

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