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Torsionfree modules and classes of orders

Published online by Cambridge University Press:  17 April 2009

William H. Gustafson
William H. Gustafson
Affiliation:
Department of Mathematics, Indiana University, Indiana, USA.
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Abstract

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It is shown how torsionfree modules can be used to characterize certain important classes of orders over Dedekind rings. In particular, we show that an order is Gorenstein if and only if each of its lattices can be embedded as a pure sublattice of a free lattice. We also show that an order is hereditary if and only if the tensor product of any of its right lattices with any of its left lattices is torsionfree over the ground domain.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 3 , December 1974 , pp. 365 - 371
Copyright
Copyright © Australian Mathematical Society 1974

References

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