Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T04:13:08.684Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-sided localization in semiprime FBN rings

Published online by Cambridge University Press:  17 April 2009

M. H. Upham
M. H. Upham
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, USA.
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.

The main result of this paper is that the left- and right-quotient rings at a hereditary link closed set of prime ideals of a semiprime fully bounded Noetherian (FBN) ring coincide. This was a result already known for nonsemiprime FBN rigns, but a question left open in the semiprime case. A cornerstone of our approach is that the torsion theory determined by a link-closed hereditary set of prime ideals in an FBN ring is “nice”, but not necessarily perfect. Some conditions which do produce perfect torsion theories are investigated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 2 , October 1984 , pp. 179 - 191
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Beachy, J.A., “Stable torsion radicals over FBN rings”, J. Pure Appl. Algebra 24 (1982), 227–233.Google Scholar
[2]Faith, C., Injective modules and injective quotient rings (Lecture Notes in Pure and Applied Mathematics, 72. Marcel Dekker, New York, 1982).Google Scholar
[3]Jategaonkar, A.V., “Jacobson's conjecture and modules over fully bounded Noetherian prime rings”, J. Algebra 30 (1974), 103–121.Google Scholar
[4]Lambek, J., “Bicommutators of nice injectives”, J. Algebra 21 (1972), 60–73.CrossRefGoogle Scholar
[5]Lambek, J. and Michler, G., “Localization of right Noetherian rings at semiprime ideals”, Canad. J. Math. 26 (1974), 1069–1085.Google Scholar
[6]Müller, B.J., “Localization in fully bounded Noetherian rings”, Pacific J. Math. 67 (1976), 233–245.Google Scholar
[7]Müller, B.J., “Two-sided localization in Noetherian PI rings”, J. Algebra 63 (1980), 359–373.Google Scholar
[8]Müller, B.J., “Links between maximal ideals in bounded Noetherian prime rings of Krull dimension one”, preprint.Google Scholar
[9]Richards, R., “Noetherian prime rings of Krull dimension 1“ (PhD Thesis, McMaster University, Hamilton, Ontario, 1977).Google Scholar
[10]Stenstrom, B., Rings and modules of quotients (Lecture Notes in Mathematics, 237. Springer-Verlag, Berlin, Heidelberg, New York, 1971).Google Scholar
[11]Upham, M., “Right localizable multiplicative sets and prime ideals of FBN rings”, Comm. Algebra 9 (1981), 1093–1103.CrossRefGoogle Scholar