3 ms·

The Krull dimension of the semiring of natural numbers is equal to 2

• OgsyedIE 1y ago
  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 1y ago
  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.
  • macrolocal 1y ago
    By analogy with stacks, my intuition is that Spec(N) still has a one-dimensional geometry, but with a (-1)-dimensional tier from quotienting out the prime points by a semiring action.
• MarkusQ 1y ago
  > 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.
• lovich 1y ago
  Is there a good primer anywhere on how to read these types of mathematical proofs? I can kinda follow along with a lot of them when it’s translated to English, but I have no idea what most of the symbols mean or even enough info to google for the things I don’t quite understand