A note on Laskerian rings

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. © pakistan academy of sciences.