  We shall study three subjects of the Jacobi-Perron Algorithm of dimension 2.
First, we study the "ideal convergence". About the approximations (p_n/r_n,
q_n/r_n) to (A, B) (where A and B are positive real numbers, r_n, p_n and q_n
are natural numbers), Showing some inequalities and evaluations of |p_n-Ar_n|
and |q_n-Br_n|, we shall prove some sufficient conditions for p_n-Ar_n and
q_n-Br_n converge at 0, in which case the algorithm is said to be ideally
convergent(see [1]). Second, in connection with the classical continued
fractions, we treat the behavior of the algebraic conjugates. Third, we shall
prove that the set of (A, B) for which the digits of expansions are bounded
from above is null which is a generalization of Theorem 196 in [3].
