EXAMPLES OF CHAIN DOMAINS

Authors
MAZUREK R ROSZKOWSKA E
Citation
R. Mazurek et E. Roszkowska, EXAMPLES OF CHAIN DOMAINS, Proceedings of the American Mathematical Society, 126(3), 1998, pp. 661-667
Citations number
11
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
126
Issue
3
Year of publication
1998
Pages
661 - 667
Database
ISI
SICI code
0002-9939(1998)126:3<661:>2.0.ZU;2-M
Abstract
Let gamma be a nonzero ordinal such that alpha + gamma = gamma for eve ry ordinal alpha < gamma. A chain domain R (i.e. a domain with linearl y ordered lattices of left ideals and right ideals) is constructed suc h 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 pr ovides answers to some open questions.