The orthogonal group over a full ring

Congruence of Symmetric Inner Products Over finite Commutative Rings of Odd Characteristic

“…First, we shall concentrate on a finite local ring of odd characteristic. McDonald and Hershberger [5] proved the following theorem. We write H 2ν = 0 I ν I ν 0 .…”

The symplectic group over a ring with one in its stable range

“…Stable range one rings (both commutative and noncommutative) have been examined from a ring theoretic viewpoint in [3], [4], [5], and [20]. The role that stable range one rings play in linear algebra and the general linear group is discussed in [1], [4], [7], [15], [21] , a n in R with…”

“…If F is a symplectic space of dimension 2 over a commutative ring with stable range one, then Sp (V) is precisely the special linear group SL(F) of V. In this case, the structure of SL(F) is given in [15]. PROPOSITION …”

“…It is easy to see that R/A has stable range one if R has stable range one, e.g., see (Prop. 2.6(a) of [14]). In turn, π A induces a group morphism π A : We now study the commutator subgroup of Sp(F).…”