ILI-ideals and prime LI-ideals in lattice implication algebras

Authors:
Yong Lin Liu;San Yang Liu;Yang Xu;Ke Yun Qin
Affiliations:
Department of Applied Mathematics, Xidian University, Xi'an 710071, Shaanxi, PR China and Department of Mathematics, Nanping Teachers College, Nanping 353000, Fujian, PR China;Department of Applied Mathematics, Xidian University, Xi'an 710071, Shaanxi, PR China;Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China;Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China
Venue:
Information Sciences: an International Journal
Year:
2003

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Abstract

The notions of ILI-ideals and maximal LI-ideals of lattice implication algebras are introduced, respectively. The properties of ILI-ideals, prime LI-ideals and maximal LI- ideals are investigated. Several characterizations of ILI-ideals and prime LI-ideals are given. The extension theorem of ILI-ideals is obtained. The relations between ILI-ideals and LI-ideals, between ILI-ideals and implication filter, between prime LI-ideals and maximal LI-ideals, between prime LI-ideals and ILI-ideals, between maximal LI-ideals and ILI-ideals, between maximal LI-ideals and LI-ideals, and between prime LI-ideals and LI-ideals are investigated, respectively. Some classes of lattice implication algebras are characterized by their ILI-ideals (respectively prime LI-ideals, maximal LI-ideals).