{AB} is a superkey, but it's not a candidate key. (It's not a minimal superkey.) The decomposition
- R1(A B)
- R2(B C)
is in at least BCNF.
Informally, a relation is in BCNF if every arrow is an arrow out of a candidate key. B is a candidate key in R2.
The relation R is not in BCNF. The only candidate key in R is A; the FD B->C has an arrow that's not out of a candidate key.
In truth, both R1 and R2 are much stronger than BCNF. They're both in 6NF.