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19 lines
797 B
Markdown
19 lines
797 B
Markdown
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# comm_alg
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SLMath collaboration for adding Krull dimension and Hilbert polynomial to mathlib
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We start the comm algebra project by important definitions and theorems and go from there.
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Feel free to add, modify, and expand this file. Below are starting point for the project:
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Definitions of an ideal, prime ideal, and maximal ideal
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Definition of a Spec of a ring
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Definition of a Noetherian and Artinian rings
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Definition of a local ring and quotient ring
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Definition of the Krull dimension
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Give examples of each of the above cases for a particular instances of ring
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Theorem 0: Hilbert Basis Theorem
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Theorem 1: If A is a nonzero ring, then dim A[t] >= dim A +1
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Theorem 2: If A is a nonzero noetherian ring, then dim A[t] = dim A + 1
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Theorem 3: If A is nonzero ring then dim A_p + dim A/p <= dim A
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