H. You, ON SUBGROUPS OF GL(2) OVER A CLASS OF NONCOMMUTATIVE RINGS WHICH ARE NORMALIZED BY ELEMENTARY MATRICES, Chinese annals of mathematics. Ser. B, 14(4), 1993, pp. 507-514
Let R be an associative ring with 1 and Y not-equal R a quasi-ideal of
R. Set T2(R, Y) = {diag(u,v)a1,2b2,1C1,2: a+c,b is-an-element-of Y,u,
v is-an-element-of GL1R, and v-1au-a, uav-1-a is-an-element-of Y for a
ll a is-an-element-of R}. It is proved that if R satisfies 2-fold cond
ition, then [E2R,T2(R,Y)] subset-of E2(R,Y) subset-of T2(R,Y); and if
R satisfies 6-fold condition, then E2(R,Y) = [E2R,E2(R,Y)] = [E2R,T2(R
,Y)] and the sandwich theorem holds.