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Torsionfree modules and classes of orders
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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