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, G (2020). Ascending chains of ideals in the polynomial ring. Turkish Journal of Mathematics 44 (6): 2402-2414. https://doi.org/10.3906/mat-1904-61
