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A note on Cohn's universal localisation at a semiprime ideal

Published online by Cambridge University Press:  17 April 2009

John A. Beachy
John A. Beachy
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, United States of America
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The universal localisation RΓ(s) at a semiprime ideal S of a left Noetherian ring R was defined and studied by P. M. Cohn. In this note we investigate the interaction between the universal localisation RΓ(s), the Ore localisation at S, and the torsion-theoretic localisation at the injective envelope E(R/S) of the module R(R/S).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 361 - 367
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Beachy, J.A., ‘Some aspects of noncommutative localization,’, in Noncommutative Ring Theory, Kent State, 1975, Lecture Notes in Math. 545 (Springer-Verlag, Berlin, Heidelberg, New York, 1976), pp. 2–31.Google Scholar
[2]Beachy, J.A., ‘On localization at an ideal’, Canad. Math. Bull. 22 (1979), 397–401.CrossRefGoogle Scholar
[3]Beachy, J.A., ‘On inversive localization’, in Module Theory, Seattle, 1977, Lecture Notes in Math. 900 (Sprigner-Verlag, Berlin, Heidelberg, New York, 1979), pp. 46–56.Google Scholar
[4]Beachy, J.A., ‘Inversive localization at semiprime Goldie ideals’, Manuscripta Math. 34 (1981), 211–239.CrossRefGoogle Scholar
[5]Beachy, J.A., ‘On noncommutative localization’, J. Algebra 87 (1984), 213–221.CrossRefGoogle Scholar
[6]Beachy, J.A., ‘On universal localization at semiprime Goldie ideals’,in Ring Theory, Proceedings of the Biennial Ohio State-Denison Conference, May, 1992, (Jain, S.K. and Rizvi, S. Tariq, Editors) (World Scientific, Singapore, New Jersey, London, Hong Kong, 1993), pp. 41–57.Google Scholar
[7]Beachy, J.A. and Blair, W.D., ‘Localization at semiprime ideals’, J. Algebra 38 (1976), 309–314.CrossRefGoogle Scholar
[8]Cohn, P.M., ‘Inversive localisation in Noetherian rings’, Commun. Pure Appl. Math. 26 (1973), 679–691.CrossRefGoogle Scholar
[9]Cohn, P.M., Free rings and their relations, (Second edition) (Academic Press, London, New York, 1985).Google Scholar
[10]Farber, M. and Vogel, P., ‘The Cohn localization of the free group ring’, Math. Proc. Camb. Phil. Soc. 111 (1992), 433–443.CrossRefGoogle Scholar
[11]Goldie, A.W., ‘Localization in non-commutative Noetherian rings’, J. Algebra 5 (1967), 89–105.CrossRefGoogle Scholar
[12]Sheiham, D., ‘Noncommutative characteristic polynomials and Cohn localization’, J. London Math. Soc. 64 (2001), 13–28.CrossRefGoogle Scholar