Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T08:23:20.843Z Has data issue: false hasContentIssue false
  • English
  • Français

Quotient rings, chain conditions and injective ring endomorphisms

Published online by Cambridge University Press:  18 May 2009

J. C. Wilkinson
J. C. Wilkinson
Affiliation:
8 Westenra Terrace Cashmere Christchurch 2, New Zealand
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.

In this paper, the situation we shall be concerned with is that of a ring R, with a ring monomorphism α: R → R, which will not be assumed to be surjective.

Much work has been done on the skew polynomial ring R[x, α] and the skew Laurent polynomial ring R[x, x-1, α], where α is an automorphism—see [3] for example. However, the fact that α is not surjective renders the study of these objects much more difficult.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 2 , May 1989 , pp. 173 - 181
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

1.Dean, C., Monomorphisms and radicals of Noetherian rings, J. Algebra 99 (1986), 573–576.CrossRefGoogle Scholar
2.Gordon, R. and Robson, J. C., Krull dimension, Memoirs of the American Mathematical Society 133 (1973).Google Scholar
3.Jategaonkar, A. V., Skew polynomial rings over orders in Artinian rings, J. Algebra 21 (1972), 51–59.CrossRefGoogle Scholar
4.Jordan, D. A., Bijective extensions of injective ring endomorphisms, J. London Math. Soc. (2) 35 (1982), 435–448.CrossRefGoogle Scholar
5.Kerr, J. W., Ph.D. Thesis, University of California, San Diego (1979).Google Scholar
6.Warfield, R. B., Bezout rings and serial rings, Comm. Algebra, 7 (1979), 533–545.CrossRefGoogle Scholar
7.Wilkinson, J. C., Ph.D. thesis, University of Warwick (1983).Google Scholar