Mori domain
{{distinguish|Mori Domain (disambiguation){{!}}Mori Domain}}
In algebra, a Mori domain, named after Yoshiro Mori by {{harvs|txt|last=Querré|year1=1971|year2=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.Bourbaki AC ch. VII §1 no. 3 th. 2 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
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References
- {{Citation | last1=Barucci | first1=Valentina | title=On a class of Mori domains | doi=10.1080/00927878308822944 |mr=709026 | year=1983 | journal=Communications in Algebra | issn=0092-7872 | volume=11 | issue=17 | pages=1989–2001}}
- {{Citation | last1=Barucci | first1=Valentina | editor1-last=Glaz | editor1-first=Sarah|editor1-link=Sarah Glaz | editor2-last=Chapman | editor2-first=Scott T. | title=Non-Noetherian commutative ring theory | chapter-url=https://books.google.com/books?id=0tuZkZE07TEC | publisher=Kluwer Acad. Publ. | location=Dordrecht | series=Mathematics and its Applications | isbn=978-0-7923-6492-4 |mr=1858157 | year=2000 | volume=520 | chapter=Mori domains | pages=57–73}}
- {{Citation | last1=Mori | first1=Yoshiro | title=On the integral closure of an integral domain | year=1953 | journal=Memoirs of the College of Science, University of Kyoto. Series A: Mathematics | volume=27 | issue=3 | pages=249–256|url=http://projecteuclid.org/euclid.kjm/1250777561| doi=10.1215/kjm/1250777561 | doi-access=free }}
- {{Citation | last1=Nishimura | first1=Toshio | title=On the V-ideal of an integral domain. V | url=http://ci.nii.ac.jp/naid/110000160304/en |mr=0184959 | year=1964 | journal=Bulletin of the Kyoto Gakugei University. Series B, Mathematics and Natural Science | volume=25 | pages=5–11}}
- {{Citation | last1=Querré | first1=Julien | title=Sur une propiété des anneaux de Krull |mr=0299596 | year=1971 | journal=Bulletin des Sciences Mathématiques |series=2e Série | issn=0007-4497 | volume=95 | pages=341–354}}
- {{Citation | last1=Querré | first1=Julien | title=Sur les anneaux reflexifs | doi=10.4153/CJM-1975-127-5 |mr=0414537 | year=1975 | journal=Canadian Journal of Mathematics | issn=0008-414X | volume=27 | issue=6 | pages=1222–1228| doi-access=free }}
- {{Citation | last1=Querré | first1=J. | title=Cours d'algèbre | url=https://books.google.com/books/about/Cours_d_alg%C3%A8bre.html?id=X1LQAAAAMAAJ | publisher=Masson | location=Paris |mr=0465632 | year=1976| isbn=9782225441875 }}
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