Timeline for Radicals of binomial ideals
Current License: CC BY-SA 2.5
3 events
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| Dec 2, 2010 at 7:47 | comment | added | Thomas Kahle | @Timothy, I think the most opaque part of this is why the intersection of the minimal primes comes out binomial in the first place. For me it has always been useful to think about the cellular case: An ideal is cellular if in the quotient every monomial is nilpotent or regular. Cellular decompositions into binomial ideals exist in polynomial rings over every field and in characteristic zero a radical cellular ideal is just a lattice ideal + variables. (Note that in characteristic zero lattice ideals themselves radical.) | |
| Dec 1, 2010 at 21:39 | comment | added | Timothy Wagner | @Thomas: Thanks. I had already looked over your paper earlier and also used your package "binomials" in Macaulay2. It has been extremely useful, though I was curious to know if there is any abstract description of radicals of binomial ideals. I am not optimistic about as general a result as in the case of monomial ideals, but I would definitely be interested in seeing some results under additional hypothesis (like the ones I mention in the last paragraph). | |
| Dec 1, 2010 at 13:38 | history | answered | Thomas Kahle | CC BY-SA 2.5 |