“…If (R, ω) is an oriented ring of rank n, then (R, ω) has no local obstruction to being binary if the oriented ring (R ⊗ Z Z p , ω ⊗ 1) of rank n over Z p is binary for all primes p. 1 If R is an (unoriented) ring of rank n, we say that R has no local obstruction to being binary if there exists an orientation ω such that (R, ω) has no local obstruction to being binary. Since, for a ring of rank n over Z, there are exactly two possible choices of orientation, this definition naturally extends the earlier-stated notion for a ring of rank n to have no local obstruction to being monogenic.…”