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Extensions of sheaves of commutative algebras by nontrivial kernels

1974
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Pacific Journal of Mathematics
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~~~r2£~!2n· Let X be a topological space, R a sheaf of commutative algebras on X , and A a sheaf of R-modules considered as an algebra with trivial EUltiplication. It was shown in [5] that the group of equivalence classes of commutative algebra extensions of R with A as kernel is isomorphic to H 1 (R,A) , the first bicohomology group of R with coefficients in A • In this paper we will not assune·that A has trivial multiplication; we will find that, if ZA is the center of A , then H 2 (R,ZA)

doi:10.2140/pjm.1974.55.531
fatcat:5bxkavx6ejguzm2f5y5sy646ga