Abstract
Let D be an integral domain with quotient field K and D is its integral closure. (1) If D is a one dimensional Laskerian ring such that each primary ideal of D is a valuation ideal, then each overring of D is Archimedean. (2) If D is not a field, then D is a Dedekind domain if and only if D is a Laskerian almost Dedekind domain. (3) D is one dimensional Laskerian and each primary ideal of D is a valuation ideal if and only if D is one dimensional Prufer and D has finite character. In this case D is Laskerian. (4) D is one dimensional Prufer (respectively almost Dedekind) if and only if every valuation ring of K lying over D is Laskerian (respectively strongly Laskerian). (5) The complete integral closure of a pseudo-valuation domain (D, M ) is Laskerian of dimension at most one.
