Article contents
The subdirect decomposition theorem for classes of structures closed under direct limits
Published online by Cambridge University Press: 09 April 2009
Abstract
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
- 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
- 5
- Cited by