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Interesting, makes me curious about geometric ways of looking at semirings. Krull dimension is an algebraic way of capturing the dimension of corresponding geom
by 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 agoBy 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.