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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-10,
author = {W. Kucharz},
title = {Rational functions without poles in a compact set},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {119-125},
zbl = {1091.14003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-10}
}
W. Kucharz. Rational functions without poles in a compact set. Colloquium Mathematicae, Tome 106 (2006) pp. 119-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-10/