Examples of chain domains

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.