Algebras of constants for some extensions of derivations
type: Item
instance of: scholarly article
title: Algebras of constants for some extensions of derivations
zbMATH Open document ID: 1022.13005
DOI: 10.1016/S0019-3577(02)90007-8
author: Andrzej J. Maciejewski
author: Andrzej Nowicki
published in: Indagationes Mathematicae. New Series
publication date: 2003-06-05T00:00:00Z
review text: Let \(A= B[t]\) be the polynomial ring in one variable \(t\) over a unique factorization \(k\)-domain \(B\), where \(k\) is a field with \(\operatorname {char}k=0\). Given an arbitrary derivation \(\delta\) of \(B\), certain extensions \(d\) to \(A\) are considered and their rings of constants \(A^d\) are described, the most important ones being defined by \(d(b)= t^s \delta(b)\) and \(d(t)= (s+1)^{-1} \delta(\varphi)\) for any \(s\in \mathbb{N}\) and \(\varphi\in B\) with \(\delta(\varphi)\neq 0\). The same is done for \(A_0^{\overline{d}}\), where \(\overline{d}\) denotes the extension of \(d\) to the field of quotients \(A_0\) of \(A\). Among the presented applications are two new counterexamples to the 14th problem of Hilbert.
Mathematics Subject Classification ID: 13N15
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 1893631
zbMATH Keywords: derivation on polynomial ring
zbMATH Keywords: extension of derivation
zbMATH Keywords: rings of constants
reviewed by: Gerhard Kowol
MaRDI profile type: Publication
Wikidata QID: Q104405087
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full work available at URL: s0019-3577(02)90007-8
OpenAlex ID: W2036463751
description: scientific article; zbMATH DE number 1893631