Geodesic
Valuation Rings and Integral Closure
Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 327-330

Voir la notice de l'article provenant de la source Cambridge University Press

A famous theorem of Krull's is that the integral closure of an integral domain D is the intersection of the valuation domains that contain D. An example is given to show that the same result need not hold for the integral closure of a ring with zero divisors.
DOI : 10.4153/CMB-1990-054-1
Mots-clés : 13A18, 13B20 
Lucas, Thomas G. Valuation Rings and Integral Closure. Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 327-330. doi: 10.4153/CMB-1990-054-1
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[1] 1. Gräter, J., Integral closure and valuation rings with zero-divisors, Studia Sci. Math. Hung. 17 (1982), 457–458. Google Scholar

[2] 2. Griffin, M., Generalizing valuations to commutative rings, Queen's Math. Preprint No. 1970-40, Queen's Univ., Kingston, Canada, 1970. Google Scholar

[3] 3. Griffin, M., Prufer rings with zero divisors, J. reine angew. Math. 239/240 (1970), 55–67. Google Scholar

[4] 4. Huckaba, J., On valuation rings that contain zero divisors, Proc. Amer. Math. Soc. 40 (1973), 9–15. Google Scholar

[5] 5. Huckaba, J., Commutative rings with Zero Divisors, Dekker, 1988. Google Scholar

[6] 6. Krull, W., Allgeneine Beweriungstheorie, J. reine angew. Math. 167 (1932), pp. 160–196. Google Scholar

[7] 7. Marot, J., Extension de la notion d'anneau valuation, Dept. Math. Faculté des Sci. de Brest (1968), 46 pp. et 39 pp. de complements. Google Scholar

[8] 8. Samuel, P., La notion de place dans un anneau, Bull. Soc. Math. France 85 (1957), 123–133. Google Scholar

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