[HN Gopher] The Krull dimension of the semiring of natural numbe...
___________________________________________________________________
The Krull dimension of the semiring of natural numbers is equal to
2
Author : surprisetalk
Score : 25 points
Date : 2025-07-18 12:48 UTC (3 days ago)
(HTM) web link (freedommathdance.blogspot.com)
(TXT) w3m dump (freedommathdance.blogspot.com)
| OgsyedIE wrote:
| Forgive me for being rusty with this higher level of algebra, but
| isn't this just counting the degrees of freedom in Spec(Z) and
| Spec(N) respectively?
| ngriffiths wrote:
| Interesting, makes me curious about geometric ways of looking at
| semirings. Krull dimension is an algebraic way of capturing the
| dimension of corresponding geometric objects, so is there some
| way of doing that with semirings? Or any more intuitive reason
| why we'd get dimension 2 here? The papers I found in a quick
| search are way over my head.
| MarkusQ wrote:
| > such that addition distributes over multiplication:
|
| > (a+b)c=ac+bc and c(a+b)=ca+cb
|
| This is usually referred to as multiplication distributing over
| addition.
___________________________________________________________________
(page generated 2025-07-21 23:01 UTC)