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In fact, we are both wrong, and the article was correct. The ideal (0) is prime if and only if the ring is a domain. The example is not a domain, so (0) is not prime. In the case of a field, the only prime ideal is (0), because the whole ring (field) is never a prime ideal. Thus the dimension of a
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704:{\displaystyle \lbrace {\text{prime ideals }}I\subseteq {\mathfrak {p}}\varsubsetneq R\rbrace \rightleftharpoons \lbrace {\text{prime ideals }}I\varsubsetneq R_{\mathfrak {p}}\rbrace ,}
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No symbol has been specified for the Krull dimension of a ring, the definition should be changed to something like:
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Incorrect use of punctuation: (geometers call it the ring of the normal cone of I.) should be changed to
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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It's correct, because we don't count (0)? (Otherwise, the field would have the dimension 1.) --
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It seems to me that there is an error in computation of the Krull dimension of (
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section for remarks and clarifications on the many facts listed in the article.
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to denote an ideal: not only is this confusing for the reader, but the symbol
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to be the supremum of the lengths of all chains of prime ideals in
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This follows from the following observation: for any prime ideal
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109:and see a list of open tasks.
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220:(or simply
112:Mathematics
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325:. ---: -->
1009:Example
446:section
442:to the
328:schemes
315:schemes
139:on the
30:B-class
36:scale.
362:Notes
351:Notes
1173:talk
1154:talk
1150:Taku
1139:talk
1000:talk
928:(or
920:and
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444:Note
131:High
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417:at
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