Journal of Commutative Algebra

A constructive theory of minimal zero-dimensional extensions

Fred Richman

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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.

Article information

Source
J. Commut. Algebra, Volume 5, Number 4 (2013), 545-566.

Dates
First available in Project Euclid: 31 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jca/1391192656

Digital Object Identifier
doi:10.1216/JCA-2013-5-4-545

Mathematical Reviews number (MathSciNet)
MR3161746

Zentralblatt MATH identifier
1291.13016

Subjects
Primary: 13B02: Extension theory
Secondary: 03F65: Other constructive mathematics [See also 03D45]

Citation

Richman, Fred. A constructive theory of minimal zero-dimensional extensions. J. Commut. Algebra 5 (2013), no. 4, 545--566. doi:10.1216/JCA-2013-5-4-545. https://projecteuclid.org/euclid.jca/1391192656


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