Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T05:42:25.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute Retracts and Amalgamation in Certain Congruence Distributive Varieties

Part of: Varieties

Published online by Cambridge University Press:  20 November 2018

Peter Jipsen  and
Henry Rose
Peter Jipsen
Affiliation:
Department of Mathematics University of Cape Town Rondebosch 7700 Cape Town Republic of South Africa
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 if V is a congruence distributive variety whose members have one element subalgebras, then the class of absolute retracts of V is closed under direct products. If V is residually small, then a characterisation of the amalgamation class of V is given.

MSC classification

Secondary: 08B10: Congruence modularity, congruence distributivity 08B25: Products, amalgamated products, and other kinds of limits and colimits
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 309 - 313
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Bergman, C., Amalgamation classes of some distributive varieties, Algebra Universalis 20 (1985), 143–166.Google Scholar
2. Jonsson, B., Amalgamation in small varieties of lattices, (Preprint).Google Scholar
3. E.W. Kiss, L. Marki, Prohle, P. and W. Tholen, Categorical, Algebraic Properties. Compendium on amalgamation, congruence extension, endomorphisms, residual smallness and injectivity, Studia Scientiarum Mathematicarum Hungarica 18 (1983), 19–141.Google Scholar
4. Pierce, R. S., “Introduction to the theory of abstract algebras,” Holt, Rinehart and Winston, New York, Montreal, London, 1968.Google Scholar
5. Taylor, W., Residually small varieties, Algebra Universalis 2 (1972), 33–63.Google Scholar
6. Taylor, W., Products of absolute retracts, Algebra Universalis 3 (1973), 400–401.Google Scholar