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Results tagged with ac.commutative-algebra
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user 19729
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
5
votes
Accepted
Flag complexes that are shellable but not vertex decomposable
I'm very slow to respond, but have finally found some time to put your complex into GAP and examine it.
Questions on $k$-decomposability on flag complexes
There were two questions about $k$-decompos …
- 3,407
5
votes
Accepted
Reference request on Leray numbers
For question 1, the earliest reference I know is:
Ralf Fröberg, On Stanley-Reisner rings, Topics in algebra, Part 2 (Warsaw, 1988), Banach Center Publ., vol. 26, PWN, Warsaw, 1990, pp. 57–70.
(This …
- 3,407
3
votes
How a "sequentially Cohen–Macaulay" simplicial complex relates to "Cohen–Macaulay" simplicia...
This answer will give a slightly different approach to the question, in terms of depth.
A definition of a Cohen-Macaulay ring $R$ is that $\operatorname{depth} R = \dim R$. There is also a good topo …
- 3,407
3
votes
Accepted
Shedding vertex
In the case of a shedding vertex $v$, $\operatorname{reg} I(G) = \max \{ \operatorname{reg} I(G \setminus N[v]) + 1, \operatorname{reg} I(G\setminus v) \}$, by a theorem of myself and Tài Hà. So your …
- 3,407
2
votes
Regularity of special monomial ideals
Doesn't a "yes" answer for your first question follow straightforwardly from facts about the lcm lattice?
See e.g. Nevo's "Regularity of edge ideals of $C_4$ free graphs via the topology of the lcm l …
- 3,407
1
vote
lattice of subalgebras of a finite commutative algebra
(Building on Goldstern's comment:) If fields are ok, (and if you allow infinite algebras -- see comment by Mariano Suárez-Alvarez below) then the distributivity certainly does not hold.
Take e.g. a …
- 3,407