Decompositions of universal algebras by idempotent algebras
type: Item
instance of: scholarly article
title: Decompositions of universal algebras by idempotent algebras
zbMATH Open document ID: 0545.08014
DOI: 10.1007/BF01203366
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: An algebra in which every subalgebra contains a singleton subalgebra (exactly one singleton subalgebra) is called an algebra with units (resp. a one-unit-algebra). Let K be a class of algebras. The Mal'tsev products \(U_{\dot K}V\), \(V_{\dot K}U\) are studied, where U is a class of one- unit-K-algebras and V is a class of idempotent K-algebras, so as the intersection \(U_{\dot K}V\cap V_{\dot K}U\). The classes K, U, V are assumed to satisfy some natural conditions. Some consequences for semigroups and quasigroups are obtained. Remark of the reviewer. The author obviously doesn't know the corresponding papers of \textit{I. I. Mel'nik} [Issled. Algebr., 32-40 (1969; Zbl 0265.08003); Teor. Polugrupp Prilozh. 3, 59-63 (1974; Zbl 0353.08002)], in which some results of the author were obtained. See also the reviewer's remark in Zbl 0537.08005 on the author's paper in Trans. Am. Math. Soc. 281, 309-321 (1984).
Mathematics Subject Classification ID: 08C10
Mathematics Subject Classification ID: 08B05
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 20M07
zbMATH DE Number: 3867411
zbMATH Keywords: class of algebras
zbMATH Keywords: Mal'tsev products
zbMATH Keywords: one-unit-K-algebras
zbMATH Keywords: idempotent K- algebras
author: Awad A. Iskander
reviewed by: Grigori I. Zhitomirski
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01203366
OpenAlex ID: W2010414291
description: scientific article; zbMATH DE number 3867411