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| In [[algebraic geometry]] and [[commutative algebra]], a [[ring homomorphism]] <math>f:A\to B</math> is called '''formally smooth''' (from [[French language|French]]: '''Formellement lisse''') if it satisfies the following infinitesimal lifting property:
| | Hello, I'm Annette, a 21 year old from Greaker, Norway.<br>My hobbies include (but are not limited to) Herpetoculture, Basket Weaving and watching NCIS.<br><br>My page ... [http://naughty.busty-xxx-babes.com/archives-2011-09/ Hdporn.Com] |
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| Suppose ''B'' is given the structure of an ''A''-algebra via the map ''f''. Given a commutative ''A''-algebra, ''C'', and a [[nilpotent ideal]] <math>N\subseteq C</math>, any ''A''-algebra homomorphism <math>B\to C/N</math> may be lifted to an ''A''-algebra map <math>B \to C</math>. If moreover any such lifting is unique, then ''f'' is said to be '''formally etale'''.
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| <ref name="four one">{{EGA|book=4-1| pages = 5–259}}</ref> <ref name="four four">{{EGA|book=4-4| pages = 5–361}}</ref>
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| Formally smooth maps were defined by [[Alexander Grothendieck]] in [[Éléments de géométrie algébrique]] IV. Among other things, Grothendieck proved that any such map is [[Flat module|flat]].<ref name="four one">{{EGA|book=4-1| pages = 5–259}}</ref>
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| ==References==
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| {{Reflist}}
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| [[Category:Commutative algebra]]
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| [[Category:Algebraic geometry]]
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Latest revision as of 23:04, 27 August 2014
Hello, I'm Annette, a 21 year old from Greaker, Norway.
My hobbies include (but are not limited to) Herpetoculture, Basket Weaving and watching NCIS.
My page ... Hdporn.Com