Gorenstein orders

Christian U. Jensen; Anders Thorup

doi:10.1016/j.jpaa.2014.05.013

Gorenstein orders

Christian U. Jensen, Anders Thorup

Department of Mathematical Sciences

3 Citations (Scopus)

Abstract

After a survey of basic characterizations and properties of one-dimensional Gorenstein rings we consider the classical orders in algebraic number fields in a very general setup. We point out connections between Gorenstein properties and properties of orders first introduced by Dedekind and Noether. Some results going back to Dedekind-Noether-Grell are slightly extended and presented in a more modern/homological language.In the final sections particular emphasis is on explicit families and examples of Gorenstein orders and the number of generators for ideals.

Original language	English
Journal	Journal of Pure and Applied Algebra
Volume	219
Issue number	3
Pages (from-to)	551-562
Number of pages	12
ISSN	0022-4049
DOIs	https://doi.org/10.1016/j.jpaa.2014.05.013
Publication status	Published - 1 Mar 2015

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abstract = "After a survey of basic characterizations and properties of one-dimensional Gorenstein rings we consider the classical orders in algebraic number fields in a very general setup. We point out connections between Gorenstein properties and properties of orders first introduced by Dedekind and Noether. Some results going back to Dedekind-Noether-Grell are slightly extended and presented in a more modern/homological language.In the final sections particular emphasis is on explicit families and examples of Gorenstein orders and the number of generators for ideals.",

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AU - Thorup, Anders

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AB - After a survey of basic characterizations and properties of one-dimensional Gorenstein rings we consider the classical orders in algebraic number fields in a very general setup. We point out connections between Gorenstein properties and properties of orders first introduced by Dedekind and Noether. Some results going back to Dedekind-Noether-Grell are slightly extended and presented in a more modern/homological language.In the final sections particular emphasis is on explicit families and examples of Gorenstein orders and the number of generators for ideals.

U2 - 10.1016/j.jpaa.2014.05.013

DO - 10.1016/j.jpaa.2014.05.013

M3 - Journal article

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VL - 219

SP - 551

EP - 562

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -

Gorenstein orders

Abstract

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