Pfaffian ideals of ladders
type: Item
instance of: scholarly article
title: Pfaffian ideals of ladders
zbMATH Open document ID: 0899.13014
DOI: 10.1016/S0022-4049(96)00125-9
author: Emanuela De Negri
published in: Journal of Pure and Applied Algebra
publication date: 1998-03-24T00:00:00Z
review text: Let \(X\) be a skew symmetric matrix of indeterminates over a field \(K\). A ladder \(Y\) of \(X\) is a union of a set of skew symmetric submatrices of \(X\). This paper concerns the study of the ideal \(I_{2t} (Y)\) of \(K[Y]\) generated by the \(2t\)-Pfaffians of \(Y\) and its coordinate ring \(R_{2t} (Y)= K[Y]/I_{2t} (Y)\). The author proves that the set of \(2t\)-Pfaffians of \(Y\) is a Gröbner basis of \(I_{2t} (Y)\) and obtains as a consequence that \(R_{2t}(Y)\) is a Cohen-Macaulay normal domain, moreover she characterizes those which are Gorenstein rings.
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 1121680
zbMATH Keywords: Pfaffian ideal
zbMATH Keywords: ladder
zbMATH Keywords: Gröbner basis
zbMATH Keywords: Cohen-Macaulay normal domain
zbMATH Keywords: Gorenstein rings
reviewed by: Marcel Morales
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121680