\(p\)-pseudosimple algebras
type: Item
instance of: scholarly article
title: \(p\)-pseudosimple algebras
zbMATH Open document ID: 0804.08002
DOI: 10.1007/BF02261730
author: A. Yu. Denisov
author: A. G. Pinus
published in: Algebra and Logic
publication date: 1994-04-12T00:00:00Z
review text: An algebra \({\mathfrak A}\) is called simple if it has only two congruences, 0 and 1; it is called pseudosimple if for any of its congruences \(\mu\neq 1\), we have \({\mathfrak A}\cong {\mathfrak A}/\mu\); it is called quasisimple if for any of its congruences \(\mu\neq 1\), there exists \(\mu'\geq \mu\) with \({\mathfrak A}\cong {\mathfrak A}/\mu'\). The last two notions were studied by H. Andréka, J. Németi and A. G. Pinus, respectively. In this paper, the authors introduce the notion of \(p\)-pseudo-simplicity by the requirement that \({\mathfrak A}\cong {\mathfrak A}/\mu\) for all principal congruences \(\mu\) of \({\mathfrak A}\). This is a generalization of pseudo-simplicity which is independent of quasi-simplicity. The authors give some properties of this notion and in particular they prove that \({\mathfrak A}\) is \(p\)-pseudosimple iff any of its homomorphic images is an epilimit of some system of isomorphic copies of \({\mathfrak A}\).
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08B25
zbMATH DE Number: 536682
zbMATH Keywords: congruences
zbMATH Keywords: pseudo-simplicity
zbMATH Keywords: quasi-simplicity
reviewed by: Ernest Płonka
MaRDI profile type: Publication
cites work: Q4146772
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full work available at URL: https://doi.org/10.1007/bf02261730
OpenAlex ID: W2038203882
description: scientific article; zbMATH DE number 536682