Hostname: page-component-669899f699-2mbcq Total loading time: 0 Render date: 2025-04-24T17:30:49.301Z Has data issue: false hasContentIssue false
  • English
  • Français

Torsion and protorsion modules over free ideal rings

Published online by Cambridge University Press:  09 April 2009

P. M. Cohn
P. M. Cohn
Affiliation:
Bedford CollegeRegents ParkLondonN.W. 1
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.

Free ideal rings (or firs, cf. [2, 3] and § 2 below) form a noncommutative analogue of principal ideal domains, to which they reduce in the commutative case, and in [3] a category TR of right R-modules was defined, over any fir R, which forms an analogue of finitely generated torsion modules. The category TR was shown to be abelian, and all its objects have finite composition length; more over, the corresponding category RT of left R-modules is dual to TR.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 490 - 498
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Bucur, I. and Deleanu, A., Categories and functors (London, New York, Sydney 1968).Google Scholar
[2]Cohn, P. M., ‘Free ideal rings’, J. Alg. 1 (1964) 47–69.CrossRefGoogle Scholar
[3]Cohn, P. M., ‘Torsion modules over free ideal rings’, Proc. London Math. Soc. (3) 17 (1967) 577–599.CrossRefGoogle Scholar
[4]Cohn, P. M., ‘Bound modules over hereditary rings’, to appear.Google Scholar
[5]Gabriel, P., ‘Des categories abeliennes’, Bull. Soc. Math. France 90 (1962) 323–448.CrossRefGoogle Scholar
[6]Gabriel, P. and Oberst, U., ‘Spektralkategorien und reguläre Ringe im von Neumannschen Sinn’, Math. Zeits. 92 (1966) 389–395.CrossRefGoogle Scholar
[7]Lambek, J., Lectures on rings and modules (Waltham Mass., Toronto and London 1966).Google Scholar
[8]Roos, J. E., ‘Locally distributive categories and strongly regular rings’, Reports of the Midwest Category Seminar (Springer Lecture Notes in Mathematics, No. 47).Google Scholar