Bijections and homomorphisms

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1984 Germany English Publisher:Springer Science and Business Media LLCJournal:Semigroup Forum, volume 28, pages 373-374 (issn: 0037-1912, eissn: 1432-2137,

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Authors: Johnson, J.; Moss, K.;

doi: 10.1007/bf02572499

Bijections and homomorphisms

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Abstract

Conditions on a map \(f:L\to M\) from a lattice L to a lattice M are considered under which f is a homomorphism of lattices in the case when f is a bijection. The main result of the paper is the following Theorem 4. Let L and M be lattices and let f:\(L\to M\) be a bijection. Then the following are equivalent: (a) f preserves meets, (b) f preserves joins, (c) f is an isomorphism. Here the equivalence of (a) and (b) seems to be a new result.

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Germany

Related Organizations

DigiZeitschriften
Germany
University of Houston
United States

Keywords

510.mathematics, homomorphism of lattices, bijection, Structure theory of lattices, Representation theory of lattices, Article

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