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Torsion theories and coherent rings

Published online by Cambridge University Press:  17 April 2009

J.M. Campbell
J.M. Campbell
Affiliation:
Canberra College of Advanced Education, Canberra, ACT.
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Abstract

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Chase has given several characterizations of a right coherent ring, among which are: every direct product of copies of the ring is left-flat; and every finitely generated submodule of a free right module is finitely related. We extend his results to obtain conditions for the ring of quotients of a ring with respect to a torsion theory to be coherent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 2 , April 1973 , pp. 233 - 239
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Chase, Stephen U., “Direct products of modules”, Trans. Amer. Math. Soc. 97 (1960), 457–473.CrossRefGoogle Scholar
[2]Stenström, Bo, Rings and modules of quotients (Lecture Notes in Mathematics, 237. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar