Varieties of Birkhoff systems. I
type: Item
instance of: scholarly article
title: Varieties of Birkhoff systems. I
zbMATH Open document ID: 1362.08002
author: John Harding
author: Anna Romanowska
published in: Order
publication date: 2017-04-20T00:00:00Z
review text: A Birkhoff system is an algebra with two binary operations \(+\) and \(\cdot\) which are commutative, associative, idempotent and satisfy the identity \(x\cdot(x+y)=x+(x\cdot y)\). Examples of Birkhoff systems are lattices, quasilattices and the regularization of the variety of lattices. The authors study the lattice of subvarieties of Birkhoff systems. In particular, they investigate splitting varieties, varieties which form a bottom of the lattice of varieties of Birkhoff systems, quasilattices, distributive bisemilattices, varieties generated by bichains, splitting pairs and varieties generated by three element bichains.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 6706483
zbMATH Keywords: Birkhoff system
zbMATH Keywords: variety
zbMATH Keywords: splitting
zbMATH Keywords: projective
zbMATH Keywords: quasilattice
describes a project that uses: Mace4
describes a project that uses: Prover9
MaRDI profile type: Publication
full work available at URL: s11083-016-9388-x
OpenAlex ID: W2330879121
cites work: Locally finite varieties.
cites work: Q5789040
cites work: Q3934450
cites work: Q3939863
cites work: Q3037496
cites work: Q3988091
cites work: Q5459443
cites work: Varieties of Birkhoff systems. II
cites work: The variety generated by the truth value algebra of type-2 fuzzy sets
cites work: Projective bichains
cites work: Varieties of lattices
cites work: Q3893986
cites work: Equational Bases and Nonmodular Lattice Varieties
cites work: Q3852235
cites work: Regular Identities in Lattices
cites work: On a method of construction of abstract algebras
cites work: On distributive quad-lattices
cites work: On equational classes of abstract algebras defined by regular equations
cites work: Q4029633
cites work: On bisemilattices with one distributive law
cites work: Q3893987
cites work: Q3941459
cites work: Q3663362
cites work: Q3037495
cites work: ON SOME CONSTRUCTIONS OF BISEMILATTICES
cites work: DISSEMILATTICES WITH MULTIPLICATIVE REDUCTS CHAINS
cites work: Q4864490
cites work: Bisemilattices of subsemilattices
cites work: Q4789441
DOI: 10.1007/S11083-016-9388-X
description: scientific article; zbMATH DE number 6706483