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Four-fold torsion theories

Published online by Cambridge University Press:  17 April 2009

Edgar A. Rutter Jr
Edgar A. Rutter Jr
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA.
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In this note 4-fold torsion theories (for categories of modules) are classified by means of orthogonal pairs of comaximal ideals. Among the applications are results of Kurata concerning lengths of n-fold torsion theories and an upper bound for the number of 4-fold torsion theories over a semiperfect ring.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 1 - 8
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Jans., J.P., “Some aspects of torsion”, Pacific J. Math. 15 (1965), 1249–1259.CrossRefGoogle Scholar
[2]Kurata, Yoshiki, “On an n–fold torsion theory in the category R M”, J. Algebra 22 (1972), 559–572.CrossRefGoogle Scholar
[3]Lambek, Joachim, Lectures on rings and modules (Blaisdell, Waltham, Massachusetts; London; Toronto; 1966).Google Scholar
[4]Rutter, Edgar A. Jr, “Torsion theories over semiperfect rings”, Proc. Amer. Math. Soc. 34 (1972), 389–395.CrossRefGoogle Scholar
[5]Stenström, Bo, Rings and modules of quotients (Lecture Notes in Mathematics, 237. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar