Right cones are semigroups for which the lattice of right ideals is a chain and a left cancellation law holds; valuation rings, the cones of ordered groups, and initial segments of ordinal numbers are examples. Two such cones are associated if they have isoniorphic lattices of right ideals so that ideals, prime ideals, and completely prime ideals correspond to each other. A list of problems is discussed. In Proposition 3.11 it is proved that the canonical mapping from a right invariant right chain domainRonto the associated right holoid can be extended to a valuation from the skew fieldQ(R)of quotients ofRonto an ordered group if and only ifJa#x2286;aJfor alla#x2208;RandJ=J(R), the Jacobson radical ofR.
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