Equivalence for varieties in general and for \(\mathcal {BOOL}\) in particular
type: Item
instance of: scholarly article
title: Equivalence for varieties in general and for \(\mathcal {BOOL}\) in particular
zbMATH Open document ID: 1012.08009
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: \textit{R. McKenzie} [in: A. Ursini et al. (eds.), Logic and algebra, Lecture Notes Pure Appl. Math. 180, 211-243 (1996; Zbl 0859.08006)] has characterized the varieties equivalent to a given variety in a purely algebraic fashion. The author of the paper under review characterizes the varieties \(\mathcal {W}\) equivalent to a variety \(\mathcal {V}\) in a purely categorical way. The varieties \(\mathcal {W}\) are described as the models of those Lawvere theories which are Morita equivalent to the Lawvere theory of \(\mathcal {V}\). As an application it is shown that the varieties \({\mathcal P}_m \) of Post algebras of fixed orders \(m\) are the only varieties equivalent to the variety \(\mathcal {BOOL}\) of Boolean algebras. The results are generalized to more general classes of algebras.
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 06D25
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 18C10
zbMATH DE Number: 1899931
zbMATH Keywords: equivalences between varieties
zbMATH Keywords: Morita equivalence of Lawvere theories
zbMATH Keywords: varietal generator
zbMATH Keywords: Boolean algebras
zbMATH Keywords: Post algebras
author: Hans-E. Porst
reviewed by: Jiří Rachůnek
MaRDI profile type: Publication
full work available at URL: s000120050151
OpenAlex ID: W2067148252
DOI: 10.1007/S000120050151
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description: scientific article; zbMATH DE number 1899931