Ring-orthogonal group

Definition
Let $$n$$ be a natural number and $$R$$ be a unital ring (ring with identity element). The ring-orthogonal group $$O(n,R)$$ is defined as the group (under multiplication) of all matrices $$A$$ such that $$AA^t = I$$ where $$I$$ is the identity matrix.

When $$R$$ happens to be a field, we use the term orthogonal group.