Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T05:42:42.149Z Has data issue: false hasContentIssue false
  • English
  • Français

A remark on Gelfand duality

Published online by Cambridge University Press:  17 April 2009

Shu-Hao Sun
Shu-Hao Sun
Affiliation:
Department of Pure Mathematics, University of Sydney, New South Wales 2006, Australia
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 prove a Gelfand-Mulvey type of duality for a certain class of rings which includes the Gelfand rings. We also show that the Maximal Ideal Theorem (MIT) can be replaced by the Prime Ideal Theorem (PIT) in the original Gelfand-Mulvey duality.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 187 - 197
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Koh, K., ‘On functional representations of a ring without nilpotent elements’, Canad. Math. Bull. 14 (1971), 345–352.Google Scholar
[2]Koh, K., ‘On a representation of a strongly harmonic ring by sheaves’, Pacific J. Math. 41 (1972), 459–68.Google Scholar
[3]Lambek, J., ‘On the representation of modules by sheaves of factor modules’, Canad. Math. Bull. 14 (1971), 459–466.Google Scholar
[4]Mulvey, C., ‘A generalization of Gelfand duality’, J. Algebra 56 (1979), 499–505.Google Scholar
[5]Mulvey, C., ‘Compact ringed spaces’, J. Algebra 52 (1978), 411–436.CrossRefGoogle Scholar
[6]Mulvey, C., Representations of rings and modules, Lecture Notes in Mathematics 753, 1979.CrossRefGoogle Scholar
[7]Simmons, H., ‘Sheaf representations of strongly harmonic rings’, Proc. Royal Society of Edinburgh 99A (1985), 269–275.Google Scholar
[8]Sun, S-H., ‘Noncommutative rings in which every prime ideal is contained in a unique maximal ideal’, J. Pure Appl. Algebra 76 (1991), 179–192.Google Scholar
[9]Sun, S-H., ‘Rings in which every prime ideal is contained in a maximal right ideal’, J. Pure Appl. Algebra 78 (1992), 183–194.Google Scholar
[10]Sun, S-H. and Mulvey, C., ‘Compact representations’, (in preparation).Google Scholar