Localizations of HNP rings

Author:
James Kuzmanovich

Journal:
Trans. Amer. Math. Soc. **173** (1972), 137-157

MSC:
Primary 16A08

DOI:
https://doi.org/10.1090/S0002-9947-1972-0311699-X

MathSciNet review:
0311699

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Abstract: In this paper it is shown that every hereditary Noetherian prime ring is the intersection of a hereditary Noetherian prime ring having no invertible ideals with a bounded hereditary Noetherian prime ring in which every nonzero two-sided ideal contains an invertible two-sided ideal. Further, it is shown that this intersection corresponds to a decomposition of torsion modules over such a ring; if is an HNP ring with enough invertible ideals, then this decomposition coincides with that of Eisenbud and Robson.

If is a maximal invertible ideal of where is as above, then an overring of is constructed which is a localization of at in a ``classical sense"; that is, it is a ring of quotients with respect to a multiplicatively closed set of regular elements satisfying the Ore conditions. The localizations are shown to have nonzero radical and are also shown to satisfy a globalization theorem. These localizations are generalizations of ones constructed by A. V. Jategaonkar for HNP rings with enough invertible ideals.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0311699-X

Keywords:
Dedekind prime ring,
hereditary Noetherian prime ring,
ring of quotients,
overring,
hereditary torsion theory,
idempotent kernel functor

Article copyright:
© Copyright 1972
American Mathematical Society