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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Examples of chain domains


Authors: R. Mazurek and E. Roszkowska
Journal: Proc. Amer. Math. Soc. 126 (1998), 661-667
MSC (1991): Primary 16D15, 16D25; Secondary 16N80
DOI: https://doi.org/10.1090/S0002-9939-98-04127-6
MathSciNet review: 1423319
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Abstract: Let $\gamma $ be a nonzero ordinal such that $\alpha +\gamma =\gamma $ for every ordinal $\alpha <\gamma $. A chain domain $R$ (i.e. a domain with linearly ordered lattices of left ideals and right ideals) is constructed such that $R$ is isomorphic with all its nonzero factor-rings and $\gamma $ is the ordinal type of the set of proper ideals of $R$. The construction provides answers to some open questions.


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Additional Information

R. Mazurek
Affiliation: Institute of Mathematics, University of Warsaw, Białystok Division, Akademicka 2, 15-267 Białystok, Poland
Email: mazurek@cksr.ac.bialystok.pl

E. Roszkowska
Affiliation: Faculty of Economy, University of Warsaw, Białystok Division, Sosnowa 62, 15-887 Białystok, Poland
Address at time of publication: Faculty of Economy, University in Białystok, Warszawska 63, 15-062 Białystok, Poland

DOI: https://doi.org/10.1090/S0002-9939-98-04127-6
Received by editor(s): December 1, 1995
Received by editor(s) in revised form: August 27, 1996
Communicated by: Ken Goodearl
Article copyright: © Copyright 1998 American Mathematical Society