On closed rational functions in several variables
| dc.creator | Petravchuk, A. P. | |
| dc.creator | Iena, O. G. | |
| dc.date | 2007-01-21 | |
| dc.date | 2007-02-12 | |
| dc.date.accessioned | 2026-07-07T07:46:00Z | |
| dc.date.available | 2026-07-07T07:46:00Z | |
| dc.description | 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. | |
| dc.description | Added references, corrected some typos | |
| dc.identifier | https://arxiv.org/abs/math/0701588 | |
| dc.identifier | http://arxiv.org/abs/math/0701588 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123690 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | 26C15 | |
| dc.title | On closed rational functions in several variables | |
| dc.type | text |