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Reflexive ideals and injective modules over Noetherian v-H orders

Published online by Cambridge University Press:  20 January 2009

K. A. Brown ,
A. Haghany  and
T. H. Lenagan
K. A. Brown
Affiliation:
Department of MathematicsUniversity Of GlasgowGlasgow G12 8QWScotland
A. Haghany
Affiliation:
Department of MathematicsIsfahan University of TechnologyIsfahan, Iran
T. H. Lenagan
Affiliation:
Department of MathematicsUniversity Of EdinburghKing's BuildingsEdinburgh EH9 3JZScotland
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Abstract

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The class of prime Noetherian v-H orders is a class of Noetherian prime rings including the commutative integrally closed Noetherian domains, and the hereditary Noetherian prime rings, and designed to mimic the latter at the level of height one primes. We continue recent work on the structure of indecomposable injective modules over Noetherian rings by describing the structure of such a module E over a prime Noetherian v-H order R in the case where the assassinator P of E is a reflexive prime ideal. This description is then applied to a problem in torsion theory, so generalising work of Beck, Chamarie and Fossum.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 1 , February 1991 , pp. 31 - 43
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

1.Beck, I., Injective modules over a Krull domain, J. Algebra 17 (1971), 116–131.CrossRefGoogle Scholar
2.Brown, K. A. and Warfield, R. B. Jr., The influence of ideal structure on representation theory, J. Algebra 116 (1988), 294–315.CrossRefGoogle Scholar
3.Chamarie, M., Anneaux de Krull non commutatifs, J. Algebra 72 (1981), 210–222.CrossRefGoogle Scholar
4.Chamarie, M., Modules sur les anneaux de Krull non commutatifs, in Seminaire d'Algèbre Paul Dubreil et Marie-Paule Malliavin, 1982 (Lecture Notes in Math. 1029, Springer-Verlag, Berlin, 1983), 283–310.CrossRefGoogle Scholar
5.Fossum, R., Injective modules over Krull orders, Math. Scand. 28 (1971), 233–246.CrossRefGoogle Scholar
6.Goodearl, K. R. and Jordan, D. A., Localizations of essential extensions, Proc. Edinburgh Math. Soc. 31 (1988), 243–247.CrossRefGoogle Scholar
7.Goodearl, K. R. and Warfield, R. B. Jr., Simple modules over hereditary Noetherian prime rings, J. Algebra 57 (1979), 82–100.CrossRefGoogle Scholar
8.Jategaonkar, A. V., Localization in Noetherian Rings (London Math. Soc. Lecture Note Series, Vol. 98, Cambridge Univ. Press, Cambridge, 1986).CrossRefGoogle Scholar
9.Joseph, A. and Stafford, J. T., Modules of t-finite vectors over semisimple Lie algebras, Proc. London Math. Soc. 49 (1984), 361–384.CrossRefGoogle Scholar
10.Lenagan, T. H. and Warfield, R. B. Jr., Affiliated series and extensions of modules, J. Algebra, to appear.Google Scholar
11.Marubayashi, H., A Krull type generalisation of HNP rings with enough invertible ideals, Comm. Algebra 11 (1983), 469–499.CrossRefGoogle Scholar
12.Maury, G. and Raynaud, J., Ordres Maximaux au Sens de K. Asano (Lecture Notes in Math. 808, Springer-Verlag, Berlin, 1980).CrossRefGoogle Scholar
13.Mcconnell, J. C. and Robson, J. C., Noncommutative Noetherian Rings (Wiley-Interscience, Chichester, 1987).Google Scholar
14.Smith, S. P., Krull dimension of the enveloping algebra of sl(2,ℂ), J. Algebra 71 (1981), 89–94.CrossRefGoogle Scholar
15.Stafford, J. T., Homological properties of the enveloping algebra U(sl 2), Math. Proc. Cambridge Philos. Soc. 91 (1982), 29–37.CrossRefGoogle Scholar