Classes of commutative rings defined by special conditions

In this article, we are mainly concerned with (n,d)-Krull rings, i.e., rings in which each n-presented prime ideal has height at most d . Precisely, we show that weakly n-Von Neumann regular rings are (n-1, 0)-Krull rings. Also, we prove that (n, d)-Krull property is not local property and that R is an (n, d)-Krull ring if and only if dim (R-P) <= d for each n-presented prime ideal P of R . Finally, we construct a class of (2, d)-Krull rings which are neither (2, d-1)-Krull rings (for d = 1) nor (1, d)-Krull rings for d = 0, 1.