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Closed polynomials and saturated subalgebras of polynomial algebras
| Content Provider | Semantic Scholar |
|---|---|
| Author | Arzhantsev, Ivan Petravchuk, Anatoliy P. |
| Copyright Year | 2007 |
| Abstract | AbstractThe behavior of closed polynomials, i.e., polynomials $$ f \in \Bbbk [x_1 , \ldots ,x_n ]\backslash \Bbbk $$ such that the subalgebra $$ \Bbbk [f] $$ is integrally closed in $$ \Bbbk [x_1 , \ldots ,x_n ] $$ , is studied under extensions of the ground field. Using some properties of closed polynomials, we prove that, after shifting by constants, every polynomial $$ f \in \Bbbk [x_1 , \ldots ,x_n ]\backslash \Bbbk $$ can be factorized into a product of irreducible polynomials of the same degree. We consider some types of saturated subalgebras $$ A \subset \Bbbk [x_1 , \ldots ,x_n ] $$ , i.e., subalgebras such that, for any $$ f \in A\backslash \Bbbk $$ , a generative polynomial of f is contained in A. |
| Starting Page | 1783 |
| Ending Page | 1790 |
| Page Count | 8 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s11253-008-0037-4 |
| Alternate Webpage(s) | https://publications.hse.ru/mirror/pubs/share/direct/219130966 |
| Alternate Webpage(s) | https://doi.org/10.1007/s11253-008-0037-4 |
| Volume Number | 59 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
