Generalizations of two theorems of Ritt on decompositions of polynomial maps

Details Generalizations of two theorems of Ritt on decompositions of polynomial maps Generalizations of two theorems of Ritt on decompositions of polynomial maps

2007-11-06

arxiv.org/abs/0711.0913v2

Mathematics

Algebraic Geometry

31 pages, the definition of the monoid O is corrected, reference is added

Scientific paper

Two theorems of J. F. Ritt on decompositions of polynomials maps are generalized to a more general situation: for, so-called, reduction monoids ($(K[x], \circ)$ and $(K[x^2]x, \circ)$ are examples of reduction monoids). In particular, analogues of the two theorems of J. F. Ritt hold for the monoid $(K[x^2]x, \circ)$ of odd polynomials. It is shown that, in general, the two theorems of J. F. Ritt fail for the cusp $(K+K[x]x^2, \circ)$ but their analogues are still true for decompositions of maximal length of regular elements of the cusp.

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