Fuzzy positive implicative ordered filters of implicative semigroups.
Products of (left) ideals in selfdistributive groupoids are studied.
It is well known that an integral domain is a valuation domain if and only if it possesses only one finitary ideal system (Lorenzen -system of finite character). We prove an analogous result for root-closed (cancellative) monoids and apply it to give several new characterizations of Prüfer (multiplication) monoids and integral domains.