Identities and quasi-identities in lattices of pseudovarieties
type: Item
instance of: scholarly article
title: Identities and quasi-identities in lattices of pseudovarieties
zbMATH Open document ID: 0832.08005
published in: Russian Mathematics
publication date: 1996-01-03T00:00:00Z
review text: A class of finite universal algebras (all of the same type) is called a pseudovariety if it is closed with respect to evaluation of homomorphic images, subalgebras, and finite direct products. Theories of pseudovarieties go back to S. Eilenberg and M. P. Schützenberger. In recent years it turned into a subject of active investigations, and one of its main directions is the study of lattices of pseudovarieties. Even the definition of a pseudovariety permits to suppose a priori that the theory of pseudovarieties is closely connected with the theory of varieties. Concerning the lattices of pseudovarieties, this conjecture is confirmed by results of \textit{P. Agliano} and \textit{J. B. Nation} [J. Aust. Math. Soc., Ser. A 46, No. 2, 177-183 (1989; Zbl 0671.08007)]. On the other hand, there were obtained a number of results concerning identities and quasi-identities in lattices of varieties. In the present article we obtain a number of results concerning identities and quasi-identities in lattices of pseudovarieties by means of these two circumstances.
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 08C99
zbMATH DE Number: 815633
zbMATH Keywords: lattices of pseudovarieties
zbMATH Keywords: identities
zbMATH Keywords: quasi-identities
author: Boris Vernikov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 815633