Projective module: Difference between revisions

Revision as of 17:12, 27 February 2004

Revision as of 00:03, 28 May 2004

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If ''e'' = ''e''² is an [[idempotent]] in the ring ''R'', then ''Re'' is a projective left module over ''R''.

Submodules of projective modules need not be projective; a ring ''R'' for which every submodule of a projective left module is projective is called [[hereditary ring|left hereditary]].

Every module over a [[field (mathematics)|field]] or [[skew field]] is projective (even free). A ring over which every module is projective is called [[semisimple ring|semisimple]].

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The [[Quillen-Suslin theorem]] is another deep result; it states that if ''K'' is a [[field (mathematics)|field]] and ''R'' = ''K''[''X''₁,...,''X''_''n''] is a [[polynomial]] ring over ''K'', then every projective module over ''R'' is free.

[[es:Módulo proyectivo]]