Analogs of Jacobian conditions for subrings
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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2016
- DOI:
- 10.48550/arXiv.1601.01508
- arXiv:
- arXiv:1601.01508
- Bibcode:
- 2016arXiv160101508J
- Keywords:
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- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 13F20 (Primary);
- 14R15;
- 13N15 (Secondary)
- E-Print:
- 11 pages