[HN Gopher] The Krull dimension of the semiring of natural numbe...
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       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)
        
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 (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.
        
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