Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T02:26:28.512Z Has data issue: false hasContentIssue false
  • English
  • Français

Injectivity and related concepts in modular varieties: II. The congruence extension property

Published online by Cambridge University Press:  17 April 2009

Emil W. Kiss
Emil W. Kiss
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, 1364 Budapest, POB 127, Hungary.
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.

Varieties with enough injectives satisfy the congruence extension property (CEP). We investigate the CEP in modular varieties by using the techniques developed in the first part of the present paper. As corollaries, we obtain the results of B. Davey and J. Kollár for the congruence distributive case as well as the description of all varieties of groups and rings with CEP, given by B. Biró, E.W. Kiss and P.P. Pálfy.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 45 - 53
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Biró, B., Kiss, E.W. and Pálfy, P.P., “On the congruence extension property”, Universal algebra, 129–151 (Proc. Coll. Math. Soc. J. Bolyai, Esztergom, 1977).Google Scholar
[2]Davey, B.A., “Weak injectivity and congruence extension in congruence distributive equational classes”, Canad. J. Math. 29 (1977), 449–459.CrossRefGoogle Scholar
[3]Day, A., “A note on the congruence extension property”, Algebra Universalis 1 (1971), 234–235.Google Scholar
[4]Kiss, E.W., “Each Hamiltonian variety has the congruence extension property”, Algebra Universalis 12 (1981), 395–398.Google Scholar
[5]Kiss, E.W., “Injectivity and related concepts in modular varieties. I. Two commutator properties”, Bull. Austral. Math. Soc. 32 (1985), 33–44.CrossRefGoogle Scholar
[6]Kiss, E.W., Márki, L., Pröhle, P. and Tholen, W., “Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphisins, residual smallness and injectivity”, Studia Sci. Math. Hungar. 18 (1983), 79–141.Google Scholar
[7]Kollár, J., “Injectivity and congruence extension in congruence distributive equational classes”, Algebra Universalis 10 (1980), 21–26.CrossRefGoogle Scholar
[8]McKenzie, R., “Residually small varieties of K-rings”, Algebra Universalis 14 (1982), 181–196.CrossRefGoogle Scholar
[9]Universal algebra, 797 (Proc. Coil. Math. Soc. J. Bolyai, Esztergon, 1977).Google Scholar