Almost simple algebras
type: Item
instance of: scholarly article
title: Almost simple algebras
zbMATH Open document ID: 0839.08001
DOI: 10.1007/BF02261709
published in: Algebra and Logic
publication date: 1995-04-20T00:00:00Z
review text: Several generalizations of simple algebras have been studied in the literature. In particular, the author introduced quasisimple algebras [``On quasisimple algebras'' (Russian), in: Studies of algebraic systems vs. properties of their subsystems, 108-118 (Sverdlovsk, 1987)] and, in a joint paper with \textit{A. J. Denisov}, \(p\)-pseudosimple algebras [Algebra Logika 31, No. 6, 637-654 (1992; Zbl 0804.08002)]. In the present paper he defines and investigates further generalizations: \(p\)-quasisimple algebras (which contain the two above-mentioned classes) and \(p\)-separable algebras (lying between the \(p\)-pseudosimple and the \(p\)-quasisimple algebras). A number of structure theorems are obtained involving, e.g., the congruence lattice, quasivarieties and some model theory.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 03C60
zbMATH DE Number: 738962
zbMATH Keywords: \(p\)-pseudosimple algebras
zbMATH Keywords: \(p\)-quasisimple algebras
zbMATH Keywords: \(p\)-separable algebras
zbMATH Keywords: generalizations of simple algebras
zbMATH Keywords: congruence lattice
author: A. G. Pinus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 738962