No abstract

In this paper, we characterize maximal non-ACCP subrings R of a domain S in case (R, S) is a residually algebraic pair and R is semilocal. In this paper, we also consider a K-algebra S, a nonzero proper ideal I of S and a subring D of the field K and we determine necessary and sufficient conditions in order that D + I is a maximal non-ACCP subring of S. This gives an example of a maximal non-ACCP subring R of a domain S such that (R, S) is a normal pair and R is not semilocal.

The main purpose of this paper is to study maximal non-Mori subrings R of a domain S. We give characterizations of such domains in several cases. If the ring R is semilocal, (R, S) is a normal pair, and R is a maximal non-Mori subring of S, we give sharp upper bounds for the number of rings and the length of chains of rings in [R, S], the set of intermediate rings.