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WINTER 2013 A constructive theory of minimal zero-dimensional extensions
Fred Richman
J. Commut. Algebra 5(4): 545-566 (WINTER 2013). DOI: 10.1216/JCA-2013-5-4-545

Abstract

Chiorescu characterized the minimal zero-dimensional extensions of certain one-dimensional rings in terms of families of ideals indexed by prime ideals. In this paper we give a constructive development of these extensions, which, to achieve maximum generality, must necessarily avoid dependence on prime ideals. This forces us to develop a purely arithmetic theory. Along the way we get a characterization, in terms of the lattice of radicals of finitely generated ideals, of when a ring with primary zero-ideal has dimension at most one.

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Fred Richman. "A constructive theory of minimal zero-dimensional extensions." J. Commut. Algebra 5 (4) 545 - 566, WINTER 2013. https://doi.org/10.1216/JCA-2013-5-4-545

Information

Published: WINTER 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1291.13016
MathSciNet: MR3161746
Digital Object Identifier: 10.1216/JCA-2013-5-4-545

Subjects:
Primary: 13B02
Secondary: 03F65

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

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Vol.5 • No. 4 • WINTER 2013
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