Localization (commutative algebra): Revision history

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curprev 04:2404:24, 22 June 2025 Alsosaid1987 talk contribs m 30,586 bytes +10 No edit summary undo Tag: Visual edit
curprev 04:2204:22, 22 June 2025 Alsosaid1987 talk contribs 30,576 bytes +232 notation for localization at point x. note on nilpotent x undo Tag: Visual edit

curprev 21:1921:19, 10 December 2024 Illuc talk contribs 30,358 bytes +220 Missing localization of a module at a prime ideal undo

curprev 08:5608:56, 12 November 2024 132.76.82.126 talk 30,138 bytes −32 →Universal property: The previous sentence was not encyclopedic undo

curprev 07:0207:02, 25 July 2024 134.10.131.172 talk 30,170 bytes +4 →top: Fixed typo undo Tags: canned edit summary Mobile edit Mobile app edit Android app edit

curprev 08:0308:03, 6 May 2024 D.Lazard talk contribs 30,166 bytes −8 Reverted 1 edit by Athena.Jennings (talk): Wrong edit: it is often the case that no element of S is regular, for example when S consists of the powers of a non-regular element undo Tags: Twinkle Undo

curprev 22:1022:10, 5 May 2024 Athena.Jennings talk contribs 30,174 bytes +8 →Universal property: Corrected a minor error relevant when one attempts to localize at a multiplicative set including non-regular elements (the new property correctly handles those cases by accommodating how said non-regular elements are always mapped to 0, typically a non-unit, witnessed by the factorization of the map j through the universal quotient map of the ambient ring through the sub-ideal of its nilradical generated from the intersection of the latter and the given localizing mult... undo Tags: Reverted Mobile edit Mobile web edit

curprev 16:3316:33, 8 January 2024 D.Lazard talk contribs 30,223 bytes 0 Reverted 1 edit by Bemjanim (talk): Not a spelling mistake undo Tags: Twinkle Undo
curprev 15:3915:39, 8 January 2024 Bemjanim talk contribs m 30,223 bytes 0 spelling mistake undo Tags: Reverted Visual edit Mobile edit Mobile web edit

curprev 15:1215:12, 24 November 2023 Andy02124 talk contribs 30,223 bytes +172 sfn fix, correct cite for Atiyah/Macdonald undo

curprev 16:0416:04, 5 August 2022 Jdgilbey talk contribs 30,001 bytes +257 →General construction: add clarification of reason for t in definition of equivalence relation undo

curprev 18:3518:35, 27 January 2022 D.Lazard talk contribs 29,690 bytes −24 Changing short description from "Construction of a ring of fractions, in commutative algebra" to "Construction of a ring of fractions" (Shortdesc helper) undo
curprev 18:0618:06, 27 January 2022 BattyBot talk contribs m 29,714 bytes −6 Fixed CS1 errors: extra text: volume and general fixes undo Tag: AWB

curprev 19:4019:40, 18 September 2021 EmlynXF talk contribs m 29,717 bytes +1 continuation of the last edit -- the direct sum is not a ring →Localization at primes undo
curprev 19:3919:39, 18 September 2021 EmlynXF talk contribs m 29,716 bytes +7 Minor edit but crucial. The direct sum is a colimit while the product is a limit, and tensors commute with colimits, not limits. Because of this, the product of flat modules is not necessarily flat, while the sum is. →Localization at primes undo
curprev 17:4217:42, 18 September 2021 EureKB talk contribs 29,709 bytes +14 clarified ambiguity in the definition undo Tag: Visual edit