Some remarks on the inverse systems of polynomial modules
type: Item
instance of: scholarly article
title: Some remarks on the inverse systems of polynomial modules
zbMATH Open document ID: 0937.13005
DOI: 10.1016/S0022-4049(97)00069-8
author: Fracesco Piras
published in: Journal of Pure and Applied Algebra
publication date: 2000-05-28T00:00:00Z
review text: Let \(R=K[x_1,x_2, \dots,x_n]\) be the ring of polynomials over a field \(K\), \(I\) be an ideal of \(R\). Macaulay's inverse system [\textit{F. S. Macaulay}, ``The algebraic theory of modular systems'' (Cambridge 1916; JFM 46.0167.01)] can be considered as an \(R\)-submodule \(H\) in \(\Hom_K(R,K)\) such that \(\text{Ann} H=I\). The author generalizes this notion for the case of an \(A\)-submodule of \(A^{\ell}\), where \(A\) is an associative algebra over \(K\) with unit element. In the case \(A=R\), a finite system of generators for an inverse system is indicated with the help of the Janet theory [\textit{M. Janet}, J. Math. Pure Appl. (8) 3, 65-151 (1920; JFM 47.0440.03) and ``Leçons sur les systèmes d'équations aux dérivées partielles'' (Paris 1929; JFM 55.0276.01)].
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 1308191
zbMATH Keywords: inverse systems of polynomial modules
zbMATH Keywords: Macaulay's inverse system
zbMATH Keywords: JFM 46.0167.01
zbMATH Keywords: Janet theory
zbMATH Keywords: JFM 47.0440.03
zbMATH Keywords: JFM 55.0276.01
MaRDI profile type: Publication
cites work: Q4293528
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description: scientific article; zbMATH DE number 1308191