On ascending chains of ideals in the polynomial ring

2016/05/20 by Pastuszak, Grzegorz
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.06263

Abstract

Assume that K is a field and I₁\subsetneq ...\subsetneq I_t is an ascending chain (of length t) of ideals in the polynomial ring K[x₁,,...,x_m], for some m≥ 1. Suppose that I_j is generated by polynomials of degrees less or equal to some natural number f(j)≥ 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 t\leqB(m,f). We also discuss some possible applications of this result.

Related

• Finite numbers of initial ideals in non-Noetherian polynomial rings
• Small ideals in polynomial rings and applications
• Ideal Membership in Polynomial Rings over the Integers
• Ideals of degree one contribute most of the height
• Powers of monomial ideals and the Ratliff-Rush operation