G_n(R)S_n(R)的平延生成与极大Abel正规子群

The Production of Flat Extension of G_n(R) and S_n(R) & Maximal Abel Normal Divisor

设Ｒ是任一有单位元的环（不必是交换环），证明了Ｓｎ（Ｒ）及其混合换位子群是由平延坐成的，Ωｉ与Ｄｉ（ｉ＝１，…，ｎ－１）分别是民Ｇｎ（Ｒ）与Ｓｎ（Ｒ）的极大Ａｂｅｌ正规子群。并证明了当环Ｒ的每个元素均是Ｒ中若干个单位元之和时，Ωｉ是由αＩ（αΩＺ＊）与平延Ｔ(ｉｉ＋１)（１）生成。

Let R be any one of rings which has unit elemet (not necessarily the commutative rings). The author proves that Sn(R) and its mixed commutor groups are formed by flat extension, and are seperatcly the maximal Abel mormal divisor, is formed by and flat extension (1) when each element of ring R is the sum of a number of unit element in R.