Beschreibung:
In [16] we studied the following problems which had been asked by H. Matsumura (cf. [11]):(I)What is the difference between smoothness and J-smoothness? In particular, concerning the characterization of smoothness,(II)When is a ring A[X1 …, Xn]/a smooth over A?In this paper, according to these problems, we will study J-smoothness further when rings are noetherian as in [16].