Radicals in the class of compact right topological rings.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.16032
published in: Applied General Topology
publication date: 2014-10-09T00:00:00Z
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 54H13
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16N80
zbMATH DE Number: 6353151
zbMATH Keywords: compact right topological rings
zbMATH Keywords: simple Noetherian rings
zbMATH Keywords: simple Artinian rings
zbMATH Keywords: simple rings
zbMATH Keywords: compact rings
zbMATH Keywords: radicals
zbMATH Keywords: open maximal ideals
author: Mihail I. Ursul
author: Adela Tripe
MaRDI profile type: Publication
full work available at URL: agt.2014.2230
OpenAlex ID: W2038516560
cites work: Q5306641
cites work: Comment on the real line
cites work: Multiplications in additive compactifications of \({\mathbb N}\) and \({\mathbb Z}\)
cites work: Linear kompakte Moduln und Ringe
cites work: Q4384766
cites work: Raising idempotents
DOI: 10.4995/AGT.2014.2230
title: Radicals in the class of compact right topological rings.
review text: The paper deals with the class of compact right topological rings, the definition of which is not provided (there is only a hint, that this definition could be obtained from another paper). For the sake of understanding the topic better, the reviewer remarks that a right topological ring is a ring equipped with the topology in which the right multiplication is continuous (but the left multiplication might be discontinuous).NEWLINENEWLINE In this paper it is shown that all compact right topological simple Artinian rings of prime characteristic and all simple left Noetherian unital compact right topological rings of prime characteristic are finite. It is also shown that the operator which sends each compact right topological ring to the intersection of all of its open maximal ideals, is a radical in the class of all compact right topological rings.
reviewed by: Mart Abel
description: scientific article; zbMATH DE number 6353151