Non-embeddable simple relation algebras
type: Item
instance of: scholarly article
title: Non-embeddable simple relation algebras
zbMATH Open document ID: 0903.03039
author: K. Appert
published in: Algebra Universalis
publication date: 1998-11-23T00:00:00Z
review text: The authors try to solve (at least partially) some of the long standing problems in relation algebras. In a simple relation algebra, every element satisfying a certain condition is an atom. The question is if also the converse statement is valid. The authors give the solution in the negative. B. Jónsson proposed to find all finite simple relation algebras without simple proper extension. The authors show how to construct them in a particular case. They answer positively the problem whether there is a countable simple relation algebra that cannot be embedded in a one-generated relation algebra and solve a similar problem for \(k\)-generated simple relation algebras.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 03G15
zbMATH DE Number: 1226229
zbMATH Keywords: relation algebra
zbMATH Keywords: proper extension
zbMATH Keywords: atom
zbMATH Keywords: simple relation algebra
MaRDI profile type: Publication
full work available at URL: s000120050041
OpenAlex ID: W2085230603
DOI: 10.1007/S000120050041
description: scientific article; zbMATH DE number 1226229