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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

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