Nonstandard characterization of pseudovarieties
type: Item
instance of: scholarly article
title: Nonstandard characterization of pseudovarieties
zbMATH Open document ID: 0840.03055
DOI: 10.1007/BF01225473
published in: Algebra Universalis
publication date: 1995-07-31T00:00:00Z
review text: A pseudovariety of algebras of a given type is understood as a class of finite algebras of that type which is closed under subalgebras, homomorphic images, and finite direct products. The author uses the main principles of nonstandard analysis to provide a new approach to pseudovarieties and the nonstandard identities that define them. The main results cannot be described here, as too many new concepts have to be defined. It turns out that one can consider nonstandard varieties of algebras as counterparts of pseudovarieties. Also, a nonstandard interpretation of implicit operations is given.
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 08C99
zbMATH DE Number: 780796
zbMATH Keywords: pseudovariety of algebras
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: nonstandard identities
zbMATH Keywords: nonstandard varieties of algebras
zbMATH Keywords: implicit operations
author: V. A. Molchanov
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01225473
OpenAlex ID: W2075005736
description: scientific article; zbMATH DE number 780796