Rational functions without poles in a compact set
Volume 106 / 2006
Colloquium Mathematicum 106 (2006), 119-125
MSC: 14A05, 14E05, 13C20.
DOI: 10.4064/cm106-1-10
Abstract
Let $X$ be an irreducible nonsingular complex algebraic set and let $K$ be a compact subset of $X$. We study algebraic properties of the ring of rational functions on $X$ without poles in $K$. We give simple necessary conditions for this ring to be a regular ring or a unique factorization domain.
