Gorenstein orders

TY - JOUR

T1 - Gorenstein orders

AU - Jensen, Christian U.

AU - Thorup, Anders

PY - 2015/3/1

Y1 - 2015/3/1

N2 - 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.

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

SN - 0022-4049

VL - 219

SP - 551

EP - 562

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 3

ER -