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
- ^ Bourbaki AC ch. VII §1 no. 3 th. 2
References
- 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
 | This commutative algebra-related article is a stub. You can help Wikipedia by expanding it. |
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
- ^ Bourbaki AC ch. VII §1 no. 3 th. 2
References
- 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
|
| This commutative algebra-related article is a stub. You can help Wikipedia by expanding it. |