On the Surjectivity of Certain Maps

C. P. Anil Kumar

Published 2016-08-12Version 1

We prove in this article the surjectivity of three maps. We prove in Theorem $1$ the surjectivity of the chinese remainder reduction map associated to projective space of an ideal with a given factorization into ideals whose radicals are pairwise distinct maximal ideals. In Theorem $2$ we prove the surjectivity of the reduction map of the strong approximation type for a ring quotiented by an ideal which satisfies unital set condition. In Theorem $3$ we prove for a dedekind domain, for $k \geq 2$, the map from $k$-dimensional special linear group to the product of projective spaces of $k-$mutually comaximal ideals associating the $k-$rows or $k-$columns is surjective. Finally this article leads to three interesting questions $1, 2, 3$ mentioned in the introduction section.