Abstract
Let γ \gamma be a nonzero ordinal such that α + γ = γ \alpha +\gamma =\gamma for every ordinal α > γ \alpha >\gamma . A chain domain R R (i.e. a domain with linearly ordered lattices of left ideals and right ideals) is constructed such that R R is isomorphic with all its nonzero factor-rings and γ \gamma is the ordinal type of the set of proper ideals of R R . The construction provides answers to some open questions.
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