Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras

Chinese Quarterly Journal of Mathematics ›› 2004, Vol. 19 ›› Issue (4): 385-392.

Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras

1.Department of Mathematics, Ocean University of China, Qingdao 266003, China; 2.Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China

Received:2002-12-26 Online:2004-12-30 Published:2024-03-05
About author:WANG Xue-fang(1975-),female,native of Linyi,Shandong,Ph.D.,engages in fuzzy logic and intelligent control.
Supported by:
SupportedbytheNationalNaturalScienceFoundationofChina(60074014)；

Abstract

Abstract: Lattice implication algebra is an algebraic structure that is established by combining lattice and implicative algebra. It originated from the study on lattice-valued logic. In this paper, we characterize two special classes of lattice implication algebra, namely, subdi-rectly irreducible and directly indecomposable lattice implication algebras. Some important results are obtained.

Key words: many-valued logic, lattice implication algebra, flter, ultra-filter, prime flter

CLC Number:

O153.5

WANG Xue-fang, XU Yang, SONG Zhen-ming. Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(4): 385-392.

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Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras

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