# 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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