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Journal of the Ramanujan Mathematical Society

Volume 33, Issue 4, December 2018  pp. 335–378.

On the surjectivity of certain maps

Authors:  C. P. Anil Kumar
Author institution:Stat Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, RVCE Post, Bangalore 560 059, India

Summary:  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 ≥ 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.

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