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2004•Unpublished venueRequires access

Characterization theorem of lattice implication algebras

Michiro Kondo

Open publisher page 1 citations

Abstract

In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.

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What this paper is about

In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.

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Available abstract

In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.

Key concepts: Lattice (music), Commutative property, Mathematics, Pure mathematics, Class (philosophy), Non-associative algebra, Interior algebra, Characterization (materials science)

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