Persistence and stability properties of powers of ideals
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Publication:472996
DOI10.1016/j.jpaa.2014.05.011zbMath1305.13005arXiv1208.4684OpenAlexW1980278958MaRDI QIDQ472996
Jürgen Herzog, Ayesha Asloob Qureshi
Publication date: 21 November 2014
Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1208.4684
Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Other special types of modules and ideals in commutative rings (13C13) Combinatorial aspects of commutative algebra (05E40)
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Uses Software
Cites Work
- Unnamed Item
- Progress in commutative algebra 1. Combinatorics and homology
- Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals
- Asymptotic prime divisors
- A conjecture on critical graphs and connections to the persistence of associated primes
- The stable set of associated primes of the ideal of a graph
- Discrete polymatroids
- The stable set of associated prime ideals of a polymatroidal ideal
- Monomial localizations and polymatroidal ideals
- Associated primes of powers of edge ideals
- Monomial ideals whose depth function has any given number of strict local maxima
- The depth of powers of an ideal
- Asymptotic Stability of Ass(M/I n M)
- The asymptotic nature of the analytic spread
- Monomial Ideals
- On prime divisors of \(I^n\), \(n\) large