Turkish Journal of Mathematics
Article Title
DOI
10.3906/mat-1904-61
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.
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
