Topological nearrings whose additive groups are Euclidean
type: Item
instance of: scholarly article
title: Topological nearrings whose additive groups are Euclidean
zbMATH Open document ID: 0830.16032
DOI: 10.1007/BF01293589
published in: Monatshefte für Mathematik
publication date: 1995-07-05T00:00:00Z
full work available at URL: https://eudml.org/doc/178687
review text: The author is concerned here with additive groups with a locally compact Hausdorff topology for which the group operation is continuous. The conditions under which a multiplication can be defined on the group which makes it into a nearring or a ring are determined. After this general introduction, the special case where the group is the topological Euclidean \(n\)-group \(R^n\) is considered in detail. A family of nearrings defined on these groups are analysed in some detail. Most of the nearrings turn out to be planar. Their ideals are characterized. The multiplicative semigroups of the nearrings are considered in detail, and they are shown to be of a particularly well-behaved kind. The lattice of congruences is also determined. Finally the special case of \(R\) itself is considered. The detailed structure of the corresponding nearrings is obtained including the automorphism group.
Mathematics Subject Classification ID: 16Y30
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 22D45
zbMATH DE Number: 757759
zbMATH Keywords: locally compact Hausdorff topologies
zbMATH Keywords: nearrings
zbMATH Keywords: ideals
zbMATH Keywords: multiplicative semigroups
zbMATH Keywords: lattice of congruences
zbMATH Keywords: automorphism groups
author: jun. Kenneth D. Magill
reviewed by: John D. P. Meldrum
MaRDI profile type: Publication
cites work: Planarity in algebraic systems
cites work: Q5522002
cites work: Q4032146
cites work: Q3848243
cites work: Topological \(N\)-groups
cites work: Topological nearrings whose additive groups are tori
cites work: Q3807388
OpenAlex ID: W2911457137
description: scientific article; zbMATH DE number 757759