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exal
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There are 4 letters in EXAL ( A1E1L1X8 )
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Definitions of exal in various dictionaries:
EXAL - In algebra, Exalcomm is a functor classifying the extensions of a commutative algebra by a module. More precisely, the elements of Exalcommk(R,M) are...
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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 Exalcommk(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 Grothendieck (1964, 18.4.2). * Exalcomm is one of the AndréQuillen cohomology groups and one of the LichtenbaumSchlessinger functors. * Given homomorphisms of commutative rings A B C and a C-module L there is an exact sequence of A-modules (Grothendieck 1964, 20.2.3.1)* * * * 0 * * * Der * * B * * * * |