关于某些映射的满射性II：对于广义射影空间
On the Surjectivity of Certain Maps II: For Generalized Projective Spaces
摘要：
本文引入了广义射影空间（定义$[2.1, 2.5]$），并在两种不同的情况下证明了三个主要定理。在第一种情况下，我们证明了，在主要定理$A$，中国剩余约化映射的满射性与一个理想的广义射影空间，具有一个给定的分解成相互余极大理想，每个理想包含在100个极大理想，使用的关键概念选择乘数假设（定义$4.11$）是满意的。在$k$ -维特殊线性群到$k$ -行或$k$ -列的$k$ -互余极大理想的广义射影空间的乘积的满射性的第二个上下文中，我们在环上或广义射影空间上证明了其余两个定理.最后，在最后一节中，我们提出了开放性问题$[9.1, 9.2]$，其答案在更大的一般性是未知的。
英文摘要：
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 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 is not known.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
