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Summary
| Description |
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 |  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.
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 12:08, 10 April 2012 | | 534 × 63 (69 KB) | KonradVoelkel | removed module property, instead using "perfect rings" as suggested by RSchwieb. |
| 14:45, 5 April 2012 |  | 543 × 84 (108 KB) | KonradVoelkel | removed explicit names for rings and modules. | |
| 13:30, 5 April 2012 |  | 543 × 84 (104 KB) | KonradVoelkel | finally managed to remove strange black box (which was due to Inkscape errors) | |
| 14:54, 10 November 2011 |  | 543 × 84 (102 KB) | KonradVoelkel | still trying ... | |
| 14:47, 10 November 2011 |  | 543 × 84 (114 KB) | KonradVoelkel | 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 |
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