Universal problem for Kähler differentials in A-modules: Non-commutative and commutative cases

M. Abel () and P. P. Ntumba ()
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M. Abel: University of Tartu
P. P. Ntumba: University of Pretoria

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 4, 497-511

Abstract: Abstract Let A be an associative and unital K-algebra sheaf, where K is a commutative ring sheaf, and ε an (A, A)-bimodule, that is, a sheaf of (A, A)-bimodules. We construct an (A, A)-bimodulc which is K-isomorphic with the K-module D K (A, ε) of germs of K-derivations. A similar isomorphism is obtained, this time around with respect to A, between the K-module D K (A, ε) with the A-module Hom A (Ω K (A), ε). where A, in addition of being associative and unital, is assumed to be commutative, and Ω K (A) denotes the A-module of germs of Kähler differentials. Finally, we expound on functoriality of Kähler differentials.

Keywords: A-module, (A; A)-bimodule, K-module of germs of K-derivations, A-module of germs of Kähler differentials, locally free A-module (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0077-4

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