Institute of Mathematics, University of Warsaw, Bialystok Division, Akademicka 2, 15-267 Bialystok, Poland ; Faculty of Economy, University of Warsaw, Bialystok Division, Sosnowa 62, 15-887 Bialystok, Poland
Abstract:
Let be a nonzero ordinal such that for every ordinal . A chain domain (i.e. a domain with linearly ordered lattices of left ideals and right ideals) is constructed such that is isomorphic with all its nonzero factor-rings and is the ordinal type of the set of proper ideals of . The construction provides answers to some open questions.