Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T02:47:57.339Z Has data issue: false hasContentIssue false

Near-rings of homotopy classes of continuous functions

Published online by Cambridge University Press:  17 April 2009

Wolfgang Mutter
Affiliation:
Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1/2, D-8520 Erlangen, Germany
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.

In this paper we show that for a compact connected abelian group G the near-ring [G, G] of all homotopy classes of continuous selfmaps of G is an abstract affine near-ring, and investigate the ideal structure of these near-rings.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Eilenberg, S. and Mac-Lane, S., ‘Group extensions and homology’, Ann. of Math. 43 (1942), 757831.CrossRefGoogle Scholar
[2]Fuchs, L., Infinite abelian groups I (Academic Press, New York, San Francisco, London, 1970).Google Scholar
[3]Fuchs, L., Infinite abelian groups II (Academic Press, New York, San Francisco, London, 1973)Google Scholar
[4]Gonshor, H., ‘On abstract affine near-rings’, Pacific J. Math. 14 (1964), 12371240.CrossRefGoogle Scholar
[5]Hewitt, E. and Ross, K.A., Abstract harmonic analysis 1, Grundlehren der mathematischen Wissenschaften 115 (Springer-Verlag, Berlin, Göttingen, Heidelberg, 1963).Google Scholar
[6]Hofer, R.D., ‘Near-rings of continuous functions on disconnected groups’, J. Austral. Math. Soc. Ser. A 28 (1979), 433451.CrossRefGoogle Scholar
[7]Hofmann, K.H. and Mostert, P.S., Elements of Compact Semigroups (Charles E. Merrill Books, Columbus, Ohio, 1966).Google Scholar
[8]Hofmann, K.H., Introduction to the theory of compact groups Part I, Tulane University Lecture Notes (Dept. Math., Tulane University, 1967)Google Scholar
[9]Mutter, W., ‘Near-rings of continuous functions on compact abelian groups’, Semigroup Forum (to appear).Google Scholar
[10]Pilz, G., Near-rings, Mathematics Studies 23 (North Holland, New York, 1983).Google Scholar
[11]Scheerer, H. and Strambach, K., ‘Idempotente Multiplikationen‘, Math. Z. 182 (1983), 95119.CrossRefGoogle Scholar