On some geometrical properties defining classes of rings and varieties of modular lattices
type: Item
instance of: scholarly article
title: On some geometrical properties defining classes of rings and varieties of modular lattices
zbMATH Open document ID: 0536.06009
DOI: 10.1007/BF01194511
author: Alan Day
published in: Algebra Universalis
publication date: 1983-01-01T00:00:00Z
review text: Several authors have considered the question of translating axiomatic geometry into the language of lattice theory. For example, it is well known that the modular law distinguishes projective geometries, and Jónsson's law distinguishes desarguean projective geometries. In a previous publication, the author has considered two identities that reflect Pappus' theorem. In the present paper he considers these pappian identities more closely. He uses what he calls the quasi-plane identity to solve the problem of Skornyakov: to find a lattice equation which, when applied to \({\mathcal L}(_ RR^ 3)\) for a regular ring R, characterises the commutativity of the ring.
Mathematics Subject Classification ID: 06C10
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 51A05
zbMATH DE Number: 3851167
zbMATH Keywords: desarguean projective geometries
zbMATH Keywords: pappian identities
zbMATH Keywords: regular ring
zbMATH Keywords: commutativity
MaRDI profile type: Publication
cites work: Topological Representation of Algebras
cites work: Ein Struktursatz für ebene Verbände
cites work: Bemerkungen zu einem verbandstheoretischen Problem von Skornjakov
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cites work: Free Modular Lattices
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cites work: Q5596304
cites work: Q5537459
cites work: On free modular lattices generated by finite chains
full work available at URL: https://doi.org/10.1007/bf01194511
OpenAlex ID: W1972065390
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description: scientific article; zbMATH DE number 3851167