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comment Strengthening the Induction Hypothesis
You can also do it without induction, using a telescope sum: $\displaystyle\sum_{k=1}^{n} \frac{1}{k^2} = 1 + \sum_{k=2}^{n} \frac{1}{k^2} < 1 + \sum_{k=2}^{n} \frac{1}{k(k-1)} = 1 + 1 - \frac{1}{n} = 2 - \frac{1}{n}$.
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answered Is a composite of (co)monadic adjunctions (co)monadic?
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comment A short proof for $\dim(R[T])=\dim(R)+1$
You did answer the question "what is a short proof of the dimension formula for polynomial rings", but my question is "what is a proof of the dimension formula using the characterization of the Krull dimension by Coquand and Lombardi". It doesn't matter if you think that this characterization is necessary or not.
Mar
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comment A short proof for $\dim(R[T])=\dim(R)+1$
If you don't use it, this is not an answer to my question.
Feb
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comment A short proof for $\dim(R[T])=\dim(R)+1$
Where do you use the characterization of the Krull dimension by T. Coquand and H. Lombardi?
Feb
19
comment Representation theorem for modular lattices?
@TristanBice: What about making this an answer? :)
Feb
16
comment Representation theorem for modular lattices?
It would help me and others in how far these references answer my question, and what are the main results relevant for my question.
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comment Representation theorem for modular lattices?
Thank you. It looks nice.