Building counterexamples to generalizations for rational functions of Ritt's decomposition theorem

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dc.creatorGutierrez, Jaime
dc.creatorSevilla, David
dc.date2008-04-10
dc.date.accessioned2026-07-07T09:38:44Z
dc.date.available2026-07-07T09:38:44Z
dc.descriptionThe classical Ritt's Theorems state several properties of univariate polynomial decomposition. In this paper we present new counterexamples to Ritt's first theorem, which states the equality of length of decomposition chains of a polynomial, in the case of rational functions. Namely, we provide an explicit example of a rational function with coefficients in Q and two decompositions of different length. Another aspect is the use of some techniques that could allow for other counterexamples, namely, relating groups and decompositions and using the fact that the alternating group A_4 has two subgroup chains of different lengths; and we provide more information about the generalizations of another property of polynomial decomposition: the stability of the base field. We also present an algorithm for computing the fixing group of a rational function providing the complexity over Q.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0804.1687
dc.identifierhttp://arxiv.org/abs/0804.1687
dc.identifierJ. Algebra 303 (2006), no. 2, 655--667. MR2255128 (2007e:13032)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160913
dc.subjectCommutative Algebra
dc.subjectSymbolic Computation
dc.subject12Y05; 13P99; 68W30
dc.titleBuilding counterexamples to generalizations for rational functions of Ritt's decomposition theorem
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