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Monomial ideals with arbitrarily high tiny powers in any number of variables
Monomial ideals with arbitrarily high tiny powers in any number of variables
- Publication Year :
- 2020
- Publisher :
- Uppsala universitet, Algebra och geometri, 2020.
-
Abstract
- Powers of (monomial) ideals is a subject that still calls attraction in various ways. Let $I\subset \mathbb K[x_1,\ldots,x_n]$ be a monomial ideal and let $G(I)$ denote the (unique) minimal monomial generating set of $I$. How small can $|G(I^i)|$ be in terms of $|G(I)|$? We expect that the inequality $|G(I^2)|>|G(I)|$ should hold and that $|G(I^i)|$, $i\ge 2$, grows further whenever $|G(I)|\ge 2$. In this paper we will disprove this expectation and show that for any $n$ and $d$ there is an $\mathfrak m$-primary monomial ideal $I\subset \mathbb K[x_1,\ldots,x_n]$ such that $|G(I)|>|G(I^i)|$ for all $i\le d$.<br />9 pages, 3 figures
- Subjects :
- monomial ideals
Monomial
Algebra and Number Theory
Mathematics::Commutative Algebra
polynomial rings
Polynomial ring
010102 general mathematics
Monomial ideal
010103 numerical & computational mathematics
Mathematics - Commutative Algebra
Commutative Algebra (math.AC)
01 natural sciences
Algebra and Logic
Combinatorics
powers of monomial ideals
Minimal number of generators
FOS: Mathematics
Generating set of a group
0101 mathematics
Mathematics
Algebra och logik
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....53030f22321ed2794b44692f0fc7c2b7