Journal of the Ramanujan Mathematical Society

Volume 35, Issue 3, September 2020 pp. 241–262.

On the surjectivity of certain maps II: for generalized projective spaces

Authors: C. P. Anil Kumar
Author institution:Flat No. 104, Bldg. No. 23, Lakshmi Paradise, 5th Main, 11th Cross, Lakshmi Narayana Puram, Near Muneeswaraswamy Narasimhaswamy Temple, Bengaluru 560 021, Karnataka, India

Summary: In this article we introduce generalized projective spaces (Definitions [2.1, 2.5]) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem A, the surjectivity of the Chinese remainder reduction map associated to the generalized projective space of an ideal with a given factorization into mutually co-maximal ideals each of which is contained in only a finitely many maximal ideals, using the key concept of choice multiplier hypothesis (Definition 4.11) which is satisfied. In the second context of surjectivity of the map from k-dimensional special linear group to the product of generalized projective spaces of k-mutually co-maximal ideals associating the k-rows or k-columns, we prove remaining two main Theorems [Ω, Σ] under certain conditions either on the ring or on the generalized projective spaces. Finally in the last section we pose open Questions [9.1, 9.2] whose answers in a greater generality are not known.

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