2011•Communications in AlgebraRequires access

Monomial Derivations

Jean Moulin Ollagnier, Andrzej Nowicki

Abstract

We present some general properties of monomial derivations of the polynomial ring k[x 1,…, x n ], where k is a field of characteristic zero. The main result of this article is a characterization of some large class of monomial derivations without Darboux polynomials. In particular, we present a full description of all monomial derivations of k[x, y, z] which have no Darboux polynomials.

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Key concepts: Monomial, Mathematics, Polynomial ring, Monomial basis, Pure mathematics, Class (philosophy), Characterization (materials science), Zero (linguistics)