In algebra, a Mori domain, named after Yoshiro Mori by Querré (1971, 1976), is an integral domain satisfying the ascending chain condition on integral divisorial ideals. Noetherian domains and Krull domains both have this property. A commutative ring is a Krull domain if and only if it is a Mori domain and completely integrally closed.[1] A polynomial ring over a Mori domain need not be a Mori domain. Also, the complete integral closure of a Mori domain need not be a Mori (or, equivalently, Krull) domain.
Notes
edit- ^ Bourbaki AC ch. VII §1 no. 3 th. 2
References
edit- Barucci, Valentina (1983), "On a class of Mori domains", Communications in Algebra, 11 (17): 1989–2001, doi:10.1080/00927878308822944, ISSN 0092-7872, MR 0709026
- Barucci, Valentina (2000), "Mori domains", in Glaz, Sarah; Chapman, Scott T. (eds.), Non-Noetherian commutative ring theory, Mathematics and its Applications, vol. 520, Dordrecht: Kluwer Acad. Publ., pp. 57–73, ISBN 978-0-7923-6492-4, MR 1858157
- Mori, Yoshiro (1953), "On the integral closure of an integral domain", Memoirs of the College of Science, University of Kyoto. Series A: Mathematics, 27 (3): 249–256, doi:10.1215/kjm/1250777561
- Nishimura, Toshio (1964), "On the V-ideal of an integral domain. V", Bulletin of the Kyoto Gakugei University. Series B, Mathematics and Natural Science, 25: 5–11, MR 0184959
- Querré, Julien (1971), "Sur une propiété des anneaux de Krull", Bulletin des Sciences Mathématiques, 2e Série, 95: 341–354, ISSN 0007-4497, MR 0299596
- Querré, Julien (1975), "Sur les anneaux reflexifs", Canadian Journal of Mathematics, 27 (6): 1222–1228, doi:10.4153/CJM-1975-127-5, ISSN 0008-414X, MR 0414537
- Querré, J. (1976), Cours d'algèbre, Paris: Masson, ISBN 9782225441875, MR 0465632
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