arXiv subjects

O. G. Iena

Publications and source records attributed to O. G. Iena.

2 recordsLinked to original sources

arXiv2009

On the annihilators of rational functions in the Lie algebra of derivations of k[x, y]

Let k be an algebraically closed field of zero characteristic. The Lie algebra W_2 of all k-derivations of the polynomial ring k[x, y] naturally acts on the polynomial ring k[x, y] and also on the field of rational functions k(x, y). For a fixed non-constant rational function u from k(x,y) we consider the set A_{W_2}(u) of all derivations D from W_2 such that D(u)=0. We prove that A_{W_2}(u) is a free submodule of rank 1 of the k[x,y]-module W_2. A description of the maximal abelian subalgebras as well of the centralizers of elements in the Lie algebra A_{W_2}(u) has been obtained.

math.RA↗

arXiv2007

On closed rational functions in several variables

Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in the field k(x_1,...,x_n). We prove that a rational function F=f/g is closed if f and g are algebraically independent and at least one of them is irreducible. We also show that the rational function F=f/g is closed if and only if the pencil af+bg contains only finitely many reducible hypersurfaces. Some sufficient conditions for a polynomial to be irreducible are given.

math.RA↗