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Results tagged with prime-ideals
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user 16537
For questions involving prime ideals in commutative or noncommutative rings.
3
votes
2
answers
163
views
Weak ideal systems $r$ for which the $r$-coheight satisfies a kind of triangle inequality
Let $H$ be a multiplicatively written, commutative monoid with identity $1_H$, and let $\mathcal P(H)$ be the power set of $H$. If $X, Y \subseteq H$, we will set $$XY := \{xy: x \in X,\, y \in Y\}.$$ …
- 10.5k
0
votes
Values attained by the coheight of $(H \setminus H^\times)^k$ as a function of $H$ and $k$
This has just come to my mind: It is not an answer to the questions in the OP, but might be helpful to deal with them, so I've thought to post it as an answer (instead of adding to the OP and making i …
- 10.5k
1
vote
Accepted
Weak ideal systems $r$ for which the $r$-coheight satisfies a kind of triangle inequality
The inequality in the OP is true, and even in a stronger form: I'm indebted to Andrea Gagna for his enlightening answer, which has greatly inspired the following proofs.
Proposition. Assume $H$ is a …
- 10.5k
4
votes
1
answer
356
views
Values attained by the coheight of $(H \setminus H^\times)^k$ as a function of $H$ and $k$
Edit (Apr 24, 2017). I'm updating this post in the light of the latest developments of a related thread.
Let $H$ be a multiplicatively written, commutative monoid, and set $M := H \setminus H^\time …
- 10.5k