A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES

Algebraic systems with partial operations have different ways to interpret equality between two terms of the language. A strong identity is a formula which says that two terms are equal in the algebra if the existence of one of them implies the existence of the other one and in the case of existence...

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Autor principal:	OLIVOS,ELENA
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2008
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000200006
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spelling	oai:scielo:S0716-091720080002000062009-03-05A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIESOLIVOS,ELENAAlgebraic systems with partial operations have different ways to interpret equality between two terms of the language. A strong identity is a formula which says that two terms are equal in the algebra if the existence of one of them implies the existence of the other one and in the case of existence their values are equal. A class of partial algebras defined by a set of strong identities is called a strong variety. In the characterization of strong varieties in the case of partial algebras by means of a Birkhoff-type theorem there appeared a new concept, regularity of partial homomorphisms and partial subalgebras. Here we define and study these operators from two different perspectives. Firstly, in their relation with other well known concecpts of partial homomorphisms and partial subalgebras, as well as with the po-monoid of Pigozzi for the H, S and P operators. Secondly, in regard to the preservation of the different types of formulae that represent equality in the case of partial algebras for these operators. Finally, we give a characterization of the strong varieties as classes closed under regular homomorphisms, regular subalgebras, direct products and that satisfy a closure condition.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.27 n.2 20082008-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000200006en10.4067/S0716-09172008000200006
institution	Scielo Chile
collection	Scielo Chile
language	English
description	Algebraic systems with partial operations have different ways to interpret equality between two terms of the language. A strong identity is a formula which says that two terms are equal in the algebra if the existence of one of them implies the existence of the other one and in the case of existence their values are equal. A class of partial algebras defined by a set of strong identities is called a strong variety. In the characterization of strong varieties in the case of partial algebras by means of a Birkhoff-type theorem there appeared a new concept, regularity of partial homomorphisms and partial subalgebras. Here we define and study these operators from two different perspectives. Firstly, in their relation with other well known concecpts of partial homomorphisms and partial subalgebras, as well as with the po-monoid of Pigozzi for the H, S and P operators. Secondly, in regard to the preservation of the different types of formulae that represent equality in the case of partial algebras for these operators. Finally, we give a characterization of the strong varieties as classes closed under regular homomorphisms, regular subalgebras, direct products and that satisfy a closure condition.
author	OLIVOS,ELENA
spellingShingle	OLIVOS,ELENA A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES
author_facet	OLIVOS,ELENA
author_sort	OLIVOS,ELENA
title	A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES
title_short	A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES
title_full	A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES
title_fullStr	A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES
title_full_unstemmed	A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES
title_sort	birkhoff type theorem for strong varieties
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2008
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000200006
work_keys_str_mv	AT olivoselena abirkhofftypetheoremforstrongvarieties AT olivoselena birkhofftypetheoremforstrongvarieties
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A BIRKHOFF TYPE THEOREM FOR STRONG VARIETIES

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