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Representing Rank Complete Continuous Rings

Published online by Cambridge University Press:  20 November 2018

David Handelman
David Handelman*
Affiliation:
Justus-Liebig- Universität, Giessen, West Germany
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Given a suitable regular ring R, we construct a sheaf-like representation for R as a ring of continuous sections from a completely regular space to an appropriately toplogized disjoint union of factor rings corresponding to ‘'extremal“ pseudo-rank functions. Applied to rings which are complete with respect to a rank function this representation is an isomorphism, the completely regular space is extremally disconnected and compact, and the * ‘stalks” are the simple factor rings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1320 - 1331
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Alfsen, E. M., Compact convex sets and boundary integrals, Springer-Verlag, Band 57 (1971).Google Scholar
2. Dauns, J. and Hoffmann, K. H., Representations of rings by sections, Memoirs of the Amer. Math. Soc. 83 (1968).Google Scholar
3. Fuchs, L., Partially ordered algebraic structures (Pergamon Press, Oxford, 1963).Google Scholar
4. G∞dearl, K. R., Prime ideals in regular self-injective rings, Can. J. Math. 25 (1973), 829–839.Google Scholar
5. G∞dearl, K. R., Prime ideals in regular self-injective rings, II, J. Pure and App. Algebra 3 (1973), 357–373.Google Scholar
6. G∞dearl, K. R., Simple regular rings and rank functions, Math. Annalen 214 (1975), 267–287.Google Scholar
7. G∞dearl, K. R., Completions of regular rings, Math. Annalen 220 (1976), 229–252.Google Scholar
8. G∞dearl, K. R. and Handelman, D., Rank functions and KQ of regular rings, J. Pure and App. Algebra 7 (1976), 195–216.Google Scholar
9. Halperin, I., Regular rank rings, Can. J. Math. 17 (1965), 709–719.Google Scholar
10. Handelman, D., Perspectivity and cancellation in regular rings, J. of Algebra., to appear.Google Scholar
11. Handelman, D., Simple regular rings with a unique rank function, J. of Algebra 42 (1976), 60–80.Google Scholar
12. Handelman, D., K\ of non commutative von Neumann regular rings, J. Pure and Applied Algebra 8 (1976), 105–118.Google Scholar
13. Henriksen, M., On a class of regular rings that are elementary divisor rings, Arch. Math. 24 (1973), 133–141.Google Scholar
14. Teleman, S., On the regular rings of von Neumann, Rev. Roumaine Math. 15 (1970), 732–744.Google Scholar