Amalgamation classes of some distributive varieties
type: Item
instance of: scholarly article
title: Amalgamation classes of some distributive varieties
zbMATH Open document ID: 0572.08007
DOI: 10.1007/BF01278593
author: Clifford Bergman
published in: Algebra Universalis
publication date: 1985-01-01T00:00:00Z
review text: Let \({\mathcal H}\) be a class of algebras. Then a diagram in \({\mathcal H}\) is a quintuple \(<A,B_ 0,B_ 1,\alpha_ 0,\alpha_ 1>\) where \(A,B_ 0,B_ 1\in {\mathcal H}\) and \(\alpha_ 0\), \(\alpha_ 1\) are embeddings of A into \(B_ 0\), \(B_ 1\) respectively. The diagram is amalgamated in \({\mathcal H}\) by \(<C,\beta_ 0,\beta_ 1>\) if \(C\in {\mathcal H}\) and \(\beta_ 0\), \(\beta_ 1\) are embeddings of \(B_ 0\), \(B_ 1\) respectively into C such that \(\beta_ 0\circ \alpha_ 0=\beta_ 1\circ \alpha_ 1\). A is an amalgamation base of \({\mathcal H}\) if every \(<A,B_ 0,B_ 1,\alpha_ 0,\alpha_ 1>\) in \({\mathcal H}\) can be amalgamated in \({\mathcal H}\). The amalgamation class of \({\mathcal H}\), AMAL(\({\mathcal H})\) is the collection of all amalgamation bases of \({\mathcal H}\) and \({\mathcal H}\) has the amalgamation property of \({\mathcal H}=AMAL({\mathcal H}).\) As is well-known, very few varieties of algebras have the amalgamation property; this paper investigates the properties of amalgamation bases, particularly in varieties of lattices. The specific results obtained require too many technical definitions to be stated explicitly here.
Mathematics Subject Classification ID: 08B25
Mathematics Subject Classification ID: 06B20
Mathematics Subject Classification ID: 06D15
zbMATH DE Number: 3912451
zbMATH Keywords: diagram
zbMATH Keywords: embeddings
zbMATH Keywords: amalgamation class
zbMATH Keywords: amalgamation bases
zbMATH Keywords: amalgamation property
zbMATH Keywords: varieties of algebras
zbMATH Keywords: varieties of lattices
Wikidata QID: Q60143379
reviewed by: Sheila Oates-Williams
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3912451