A note on a theorem of Fried and MacRae
type: Item
instance of: scholarly article
title: A note on a theorem of Fried and MacRae
zbMATH Open document ID: 0983.18002
DOI: 10.1007/BF01195093
author: Josef Schicho
published in: Archiv der Mathematik
publication date: 2001-05-22T00:00:00Z
review text: The theorem of \textit{M. D. Fried} and \textit{R. E. MacRae} [Ill. J. Math. 13, 165--171 (1969; Zbl 0174.07302), Math. Ann. 180, 220--226 (1969; Zbl 0185.28803)] states that for polynomials \(L,R,l,r\) in several variables over a field \(k\) there exists a univariate polynomial \(H\) over \(k\) with \(L=H(l)\), \(R=H(r)\) iff \(l-r\) divides the polynomial \(L-R\). The authors are able to deduce this from a category theoretical statement: the pushout diagram of stable monos is also a pullback diagram (not in general but in these finitary algebraic categories they consider). As a consequence, with some additional assumptions, the authors can prove a generalized FMR-theorem for rational functions in several variables.
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 815708
zbMATH Keywords: pushout
zbMATH Keywords: stable monos
zbMATH Keywords: pullback
zbMATH Keywords: finitary algebraic categories
zbMATH Keywords: generalized FMR-theorem
zbMATH Keywords: rational functions in several variables
reviewed by: Bernd Richter
MaRDI profile type: Publication
cites work: Q3934450
cites work: On the invariance of chains of fields
cites work: On curves with separated variables
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description: scientific article; zbMATH DE number 815708