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In this study we construct, in the category XAlg(R) / A of crossed A-modules of R-algebroids, the coproduct of given two crossed A-modules M = (μ : M → A) and N = (ɳ : N → A) of R-algebroids in two different ways: Firstly we construct the coproduct M  ᴼ*  N by using the free product M * N of pre-R-algebroids M and N, and then we construct the coproduct M  ᴼ⋉  N by using the semidirect product M ⋉ N of M and N via μ. Finally we construct an isomorphism betweenM  ᴼ*  N and M  ᴼ⋉  N.

Coproduct of Crossed A-Modules of R-Algebroids