Abel, M.Ntumba, Patrice P.2014-09-232014-09-232014-08Abel, M & Ntumba, PP 2014, 'Universal problem for Kähler differentials in A-modules : non-commutative and commutative cases', Indian Journal of Pure and Applied Mathematics, vol. 45, no. 5, pp. 497-511.0019-5588 (print)0975-7465 (online)http://hdl.handle.net/2263/42073Let 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.en© Indian National Science Academy.The original publication is available at : http://link.springer.com/journal/13226.Universal problemA-modulesNon-commutativeCommutative casesPostprint Article