Timeline for Classification of commutative ring ideal closure operators?
Current License: CC BY-SA 3.0
11 events
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| Dec 13, 2021 at 21:16 | comment | added | მამუკა ჯიბლაძე | If you want to get a locale you must only consider radical ideals. | |
| Jul 23, 2015 at 15:43 | comment | added | Rex Butler | Clearly I need to learn more commutative algebra before I proceed with such a question. Thanks for your response. | |
| Jul 23, 2015 at 8:36 | comment | added | Simon Henry | Then I would say your question is too vague: there is plenty of way to do such a thing and we don't know what you want of such a notion... You can consider closure operation which are "finetely generated" in the sense that there is a finite set $P$ of element of various rings such that taking the closure of a set is to take the ideal generated by the set plus the image of element of $P$ along morphism/isomorphism. Or you can define a notion of "computable/recursive" closure operation based on the notion of recursive function etc... | |
| Jul 22, 2015 at 20:08 | comment | added | Rex Butler | That is a good argument to demostrate that there may be uncountably many closure operations. I meant to suggest only that with more conditions the set would be countable. If we are doing commutative algebra in ZFC then certainly there are only countably closure operations one can even define. I would find it fascinating if one could give some conditions, native to commutative algebra (and w.o. any high powered logic notions), that would whittle down the number of options down to a countable number. | |
| Jul 22, 2015 at 15:44 | vote | accept | Rex Butler | ||
| S Jul 22, 2015 at 14:24 | history | suggested | Pedro Sánchez Terraf | CC BY-SA 3.0 |
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| Jul 22, 2015 at 14:11 | review | Suggested edits | |||
| S Jul 22, 2015 at 14:24 | |||||
| Jul 22, 2015 at 9:38 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| Jul 22, 2015 at 9:33 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| Jul 22, 2015 at 9:19 | history | edited | Simon Henry | CC BY-SA 3.0 |
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| Jul 22, 2015 at 8:59 | history | answered | Simon Henry | CC BY-SA 3.0 |