Hostname: page-component-6bb9c88b65-dwch4 Total loading time: 0 Render date: 2025-07-24T03:17:49.588Z Has data issue: false hasContentIssue false
  • English
  • Français

On classical Krull dimension of group-graded rings

Published online by Cambridge University Press:  17 April 2009

A. V. Kelarev
A. V. Kelarev
Affiliation:
Department of Mathematics, The University of Tasmania, GPO Box 252–37, Hobart Tas 7001, Australia e-mail: kelarev@hilbert.maths.utas.edu.au
Rights & Permissions [Opens in a new window]

Extract

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.

For any ring R graded by a finite group, we give a bound on the classical Krull dimension of R in terms of the dimension of the initial component Re. It follows that if Re has finite classical Krull dimension, then the same is true of the whole ring R, too.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 255 - 259
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bell, A.D., ‘Localization and ideal theory in Noetherian strongly group-graded rings', J. Algebra 105 (1987), 76–115.CrossRefGoogle Scholar
[2]Chin, W. and Quinn, D., ‘Rings graded by polycyclic-by-finite groups’, Proc. Amer. Math. Soc. 102 (1988), 235–241.CrossRefGoogle Scholar
[3]Cohen, M. and Montgomery, S., ‘Group-graded rings, Smash products, and group actions’, Trans. Amer. Math. Soc. 282 (1984), 237–258.CrossRefGoogle Scholar
[4]Kelarev, A.V., ‘Applications of epigroups to graded ring theory’, Semigroup Forum 50 (1995), 327–350.CrossRefGoogle Scholar
[5]McConnell, J.C. and Robson, J.C., Noncommutative Noetherian rings (Wiley, New York, 1987).Google Scholar
[6]Năstăsescu, C., ‘Strongly graded rings of finite groups’, Comm. Algebra 11 (1983), 1033–1071.CrossRefGoogle Scholar
[7]Năstăsescu, C. and Van Oystaeyen, F., Graded ring theory, Math. Library 28 (North-Holland, Amsterdam, New York, 1982).Google Scholar
[8]Năstăsescu, C. and Van Oystaeyen, F., Dimensions of ring theory (Reidel, Dordrecht, 1987).CrossRefGoogle Scholar
[9]Passman, D.S., Infinite crossed products (Academic Press, New York, 1989).Google Scholar