Abstract
In 1968, Dauns and Hofmann conjectured that there should be an example of a biregular ring R (without 1) such that End(R R ) is of bounded transitivity on the maximal ideals of R but End(R R ) is not itself biregular. This note confirms the conjecture by constructing a biregular ring R all of whose Pierce stalks are copies of M 2 (D), D a division ring, while End(R R ) is not biregular. The example is one of a family of examples whose underlying space is a non-paracompact subspace of the Tychonoff plank.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W.D. Burgess and R. Raphael, Ideal extensions of rings — some topological aspects, typescript, 1994.
J. Dauns and K.H. Hofmann, The representation of biregular rings by sheaves, Math. Zeit. 91 (1966), 103–123.
J. Dauns and K.H. Hofmann, Representations of rings by sections, Memoirs Amer. Math. Soc. 83 (1968).
L. Gillman and M. Jerison, Rings of Continuous Functions, van Nostrand, Princeton, Toronto, London, New York, 1960.
R. Engelking, Outline of General Topology, North-Holland, Amsterdam, 1968.
K.R. Goodearl, von Neumann Regular Rings, Pitman, London, San Francisco, Melbourne, 1979; Second Edition, Krieger, Melbourne, FL, 1991.
S. Montgomery, Fixed rings of finite automorphism groups, Springer- Verlag, Lecture Notes in Mathematics 818 (1980).
R.S. Pierce, Modules over Commutative Regular Rings, Memoirs of the Amer. Math. Soc. 70 (1967).
R.S. Pierce, Minimal regular rings, Contemporary Math. 130 (1992), 335–348.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Burgess, W.D. (1995). Confirmation of a Conjecture of Dauns and Hofmann on Biregular Rings. In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-0443-2_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4198-0
Online ISBN: 978-94-011-0443-2
eBook Packages: Springer Book Archive