Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T07:49:01.851Z Has data issue: false hasContentIssue false

Representing varieties of algebras by algebras

Published online by Cambridge University Press:  09 April 2009

Walter D. Neumann
Affiliation:
Mathematisches Institute der Universität Bonn
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper we describe a way of representing varieties of algebras by algebras. That is, to each variety of algebras we assign an algebra of a certain type, such that two varieties are rationallv equivalent if and only if the assigned algebras are isomorphic.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Cohn, P. M., Universal Algebra (New York, 1965).Google Scholar
[2]Dale, E. C., ‘Semigroup and braid representations of varieties of algebras’, Thesis, (Manchester 1956).Google Scholar
[3]Felscher, W., ‘Equational maps’, Contrib. to Math. Logic, (Amsterdam 1968), 121161.Google Scholar
[4]Lawvere, F. W., ‘Some algebraic problems in the context of functorial semantics of algebraic theories’, Reports of the Midwest Category Seminar II, (Springer Verlag, 1968), 4161.CrossRefGoogle Scholar
[5]Linton, F. E. J., ‘Some aspects of equational categories’, Proc. Conf. Categ. Alg. La Jolla, 1965, (Springer Verlag, 1966), 8494.Google Scholar
[6]Neumann, B. H. and Wiegold, E. C., ‘A semigroup representation of varieties of algebras’, Coll. Math 14 (1966), 111114.CrossRefGoogle Scholar
[7]Neumann, W. D., ‘On cardinalities of free algebras and ranks of operations’, Arch. Math. 20 (1969), 132133.CrossRefGoogle Scholar
[8]Ostermann, F. and Schmidt, J., ‘Der baryzentrische Kalkül als axiomatische Grundlage der affinen Geometrie’, J. reine angew. Math. 224 (1966), 4457.CrossRefGoogle Scholar