Turkish Journal of Mathematics
Abstract
Assume that $K$ is a field and $I_{1}\subsetneq ...\subsetneq I_{t}$ is an ascending chain (of length $t$) of ideals in the polynomial ring $K[x_{1},...,x_{m}]$, for some $m\geq 1$. Suppose that $I_{j}$ is generated by polynomials of degrees less or equal to some natural number $f(j)\geq 1$, for any $j=1,...,t$. In the paper we construct, in an elementary way, a natural number B (m,f) (depending on $m$ and the function $f$) such that ≤ (m,f)$. We also discuss some applications of this result.
DOI
10.3906/mat-1904-61
Keywords
Polynomial rings, ascending chains of ideals, Gr\"obner bases, common invariant subspaces, quantifier elimination, quantum information theory
First Page
2402
Last Page
2414
Recommended Citation
PASTUSZAK, GRZEGORZ
(2020)
"Ascending chains of ideals in the polynomial ring,"
Turkish Journal of Mathematics: Vol. 44:
No.
6, Article 30.
https://doi.org/10.3906/mat-1904-61
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss6/30
