File:Module properties in commutative algebra.svg
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[edit]DescriptionModule properties in commutative algebra.svg |
English: Properties of modules in commutative algebras and implications between them.
References: free => projective: projective modules are exactly direct summands of free ones: Lang III.4, p. 137. projective => flat: same reason, tensor products commute with direct sums. flat => torsion-free: torsion is the kernel of M tensor (A -> Q) if Q is the total quotient ring, M the module, A the ring. module torsion-free + ring Dedekind => module flat: Liu, Corollary 1.2.14 module flat and ring perfect => module projective: wikipedia page for perfect rings module projective + ring local => module free: Matsumura, Theorem 2.5module projective + ring PID => module free: Lang, Theorem III.7.1, p. 146 and App. 2.2, p. 880 |
Date | |
Source | Own work |
Author | KonradVoelkel |
SVG development InfoField | This vector image was created with Inkscape. This file uses embedded text that can be easily translated using a text editor. |
This work is inspired by a public domain work from German wikipedia.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 12:08, 10 April 2012 | 534 × 63 (69 KB) | KonradVoelkel (talk | contribs) | removed module property, instead using "perfect rings" as suggested by RSchwieb. | |
14:45, 5 April 2012 | 543 × 84 (108 KB) | KonradVoelkel (talk | contribs) | removed explicit names for rings and modules. | ||
13:30, 5 April 2012 | 543 × 84 (104 KB) | KonradVoelkel (talk | contribs) | finally managed to remove strange black box (which was due to Inkscape errors) | ||
14:54, 10 November 2011 | 543 × 84 (102 KB) | KonradVoelkel (talk | contribs) | still trying ... | ||
14:47, 10 November 2011 | 543 × 84 (114 KB) | KonradVoelkel (talk | contribs) | trying to repair the "black boxes instead text" problem which occured due to SVG 1.2 standard issues with Inkscape ... | ||
14:38, 10 November 2011 | 543 × 84 (43 KB) | KonradVoelkel (talk | contribs) |
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Short title | Module properties (in commutative algebra) |
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