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Injectivity and related concepts in modular varieties: I. Two commutator properties

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.
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Abstract

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The first property occurred in the investigation of directly representable varieties, and was named C2 by R. McKenzie, the second one is new. Our analysis is independent of injectivity. However, in the forthcoming second part of this paper we are going to prove that varieties with enough injectives satisfy both properties, and shall use intensively the results proved here.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 1 , August 1985 , pp. 33 - 44
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Freese, R. and McKenzie, R., “The commutator, an overview”, preprint.Google Scholar
[2]Crätzer, G., General lattice theory (Birkhäuser Verlag, Basel, 1978).CrossRefGoogle Scholar
[3]Grätzer, G., Universal algebra, second edition (Springer-Verlag, Berlin, Heidelberg, New York, 1979).CrossRefGoogle Scholar
[4]Gumm, H.-P., “An easy way to the commutator in modular varieties”, Arch. Math. (Basel) 34 (1980), 220–228.CrossRefGoogle Scholar
[5]Hagemann, J. and Herrmann, C., “A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity”, Arch. Math. (Basel) 32 (1979), 234–245.CrossRefGoogle Scholar
[6]Herrmann, C., “Affine algebras in congruence modular varieties”, Acta Sci. Math. (Szeged) 41 (1979), 119–125.Google Scholar
[7]Jónsson, B., “Algebras whose congruence lattices are distributive”, Math. Scand. 21 (1967), 110–121.CrossRefGoogle Scholar