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On the associativity of the torsion functor

Published online by Cambridge University Press:  17 April 2009

John Clark
John Clark
Affiliation:
Department of Mathematics, The University of Otago, Dunedin, New Zealand.
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Let R be a commutative ring with identity. We say that tor is associative over R if for all R-modules A, B, C there is an isomorphism Our main results are that (1) tor is associative over a noetherian ring R if and only if R is the direct sum of a finite number of Dedekind rings and uniserial rings, and (2) tor is associative over an integral domain R if and only if R is a Prüfer ring.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 107 - 118
Copyright
Copyright © Australian Mathematical Society 1974

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