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The subdirect decomposition theorem for classes of structures closed under direct limits

Part of: Other classes of algebra Algebraic structures

Published online by Cambridge University Press:  09 April 2009

Xavier Caicedo
Xavier Caicedo
Affiliation:
Department of Mathematics, Universidad de los Andes, Apartado Aéreo 4976, Bogotá, D. E., Colombia
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Abstract

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By a theorem of G. Birkhoff, every algebra in an equationally defined class of algebras K is a subdirect product of subdirectly irreducible algebras of K. In this paper we show that this result is true for any class of structures. not necessarily algebraic, closed under isomorphisms and direct limits. Quasivarieties in the sense of Malcev are examples of such classes of structures. This includes Birkhoffs result as a particular case.

MSC classification

Secondary: 08A05: Structure theory 08C15: Quasivarieties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 2 , December 1980 , pp. 171 - 179
Copyright
Copyright © Australian Mathematical Society 1980

References

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