Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-14T13:21:13.112Z Has data issue: false hasContentIssue false

Mal'cev conditions, spectra and kronecker product

Published online by Cambridge University Press:  09 April 2009

Walter D. Neumann
Affiliation:
Department of Mathematics University of Maryland College Park, Md 20746USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that every possible spectrum of a Mal'cev definable class of varieties which should occur does occur. It follows that there are continuum many Mal'cev definable classes, a result also obtained by Taylor (1975) and Baldwin and Berman (1976).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

Baldwin, J. T. and Berman, J. (1976), “A model theoretic approach to Malcev conditions”, Preprint, Univ. of Illinois at Chicago Circle.Google Scholar
Freyd, P. (1966), “Algebra-valued functors in general and tensor products in particular”, Colloq. Math. 14, 89106.CrossRefGoogle Scholar
Lawvere, F. W. (1968), Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories, Reports of the Midwest Category Seminar II, Lecture Notes in Math. 61 (Springer-Verlag, Berlin, 1968), pp. 4161.Google Scholar
Neumann, W. D. (1970), “Representing varieties of algebras by algebras”, J. Austral. Math. Soc. 11, 18.CrossRefGoogle Scholar
Neumann, W. D. (1974), “On Malcev conditions”, J. Austral. Math. Soc. 17, 376384.CrossRefGoogle Scholar
Świerczkowski, S. (1964), “Topologies in free algebras”, Proc. London Math. Soc. (3) 14, 566576.CrossRefGoogle Scholar
Taylor, W. (1973), “Characterizing Mal'cev conditions”, Alg. Univ. 3, 351397.CrossRefGoogle Scholar
Taylor, W. (1975a), “Laws implying homotopy laws”, Preprint.Google Scholar
Taylor, W. (1975b), “Continuum many Mal'cev conditions”, Alg. Univ. 5, 335337.CrossRefGoogle Scholar
Taylor, W. (1975c), “The fine spectrum of a variety”, Alg. Univ. 5, 263303.CrossRefGoogle Scholar
Wille, R. (1970), Kongruenzklassengeometrien, Lecture Notes in Math. 113 (Springer-Verlag, Berlin, 1970).CrossRefGoogle Scholar