On the Surjectivity of Certain Maps

Abstract

We prove in this article the surjectivity of three maps. We prove in Theorem $1.6$ the surjectivity of the Chinese remainder reduction map associated to the projective space of an ideal with a given factorization into ideals whose radicals are pairwise distinct maximal ideals. In Theorem $1.7$ 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 $1.8$ we prove for Dedekind type domains which include Dedekind domains, for $k\ge 2$, the map from $k$-dimensional special linear group to the product of projective spaces of $k$ mutually co-maximal ideals associating the $k$-rows or $k$-columns is surjective. Finally this article leads to three interesting questions $[1.9,1.10,1.11]$ mentioned in the introduction section.

31 pages To Appear (Accepted) Journal of Ramanujan Mathematical Society, Year 2018

Cited by in corpus (5)

• On the Surjectivity of Certain Maps II: For Generalized Projective Spaces
• On the Surjectivity of Certain Maps III: The Unital Set Condition
• On a Projective Space Invariant of a Co-torsion Module of Rank Two over a Dedekind Domain
• On the Surjectivity of Certain Maps IV: For Congruence Ideal Subgroups of Type $A_k$ and $C_k$
• A Combinatorial Identity for the p-Binomial Coefficient Based on Abelian Groups