Examples of chain domains
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- by R. Mazurek and E. Roszkowska PDF
- Proc. Amer. Math. Soc. 126 (1998), 661-667 Request permission
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.References
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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
- Received by editor(s): December 1, 1995
- Received by editor(s) in revised form: August 27, 1996
- Communicated by: Ken Goodearl
- © Copyright 1998 American Mathematical Society
- 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