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In algebra, Exalcomm is a functor classifying the extensions of a commutative algebra by a module. More precisely, the elements of Exalcomm''k''(''R'',''M'') are isomorphism classes of commutative ''k''-algebras ''E'' with a homomorphism onto the ''k''-algebra ''R'' whose kernel is the ''R''-module ''M'' (with all pairs of elements in ''M'' having product 0). There are similar functors Exal and Exan for non-commutative rings and algebras, and functors Exaltop, Exantop. and Exalcotop that take a topology into account. "Exalcomm" is an abbreviation for "COMMutative ALgebra EXtension" (or rather for the corresponding French phrase). It was introduced by . Exalcomm is one of the André–Quillen cohomology groups and one of the Lichtenbaum–Schlessinger functors. Given homomorphisms of commutative rings ''A'' → ''B'' → ''C'' and a ''C''-module ''L'' there is an exact sequence of ''A''-modules : where Der''A''(''B'',''L'') is the module of derivations of the ''A''-algebra ''B'' with values in ''L''. This sequence can be extended further to the right using André–Quillen cohomology. ==References== * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Exalcomm」の詳細全文を読む スポンサード リンク
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