Analogs of Jacobian conditions for subrings

2016/01/07 by Piotr Jędrzejewicz, Janusz Zieliński, Jędrzejewicz, Piotr +1
Mathematics · #13F20 (Primary) #13N15 (Secondary) #14R15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13F20 #msc:13N15 #msc:14R15

paper · pdf · doi:10.48550/arxiv.1601.01508

11 pages

arxiv created 2016/01/07 · arxiv updated 2016/01/08

Abstract

We present a generalization of the Jacobian Conjecture for m polynomials in n variables: f1,...,fm belonging to k[x1,...,xn], where k is a field of characteristic zero and m=1,...,n. We express the generalized Jacobian condition in terms of irreducible and square-free elements of the subalgebra k[f1,...,fm]. We also discuss obtained properties in a more general setting - for subrings of unique factorization domains.

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