Geodesic
Primary Ideals in Prüfer Domains
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1024-1030

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

A Prüfer domain is an integral domain D with the property that for every proper prime ideal P of D the quotient ring DP is a valuation ring. Examples of such domains are valuation rings and Dedekind domains, a Dedekind domain being merely a noetherian Prüfer domain. The integral closure of the integers in an infinite algebraic extension of the rationals is another example of a Prüfer domain (5, p. 555, Theorem 8). This third example has been studied initially by Krull (4) and then by Nakano (8). 
Ohm, Jack. Primary Ideals in Prüfer Domains. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1024-1030. doi: 10.4153/CJM-1966-103-9
@article{10_4153_CJM_1966_103_9,
     author = {Ohm, Jack},
     title = {Primary {Ideals} in {Pr\"ufer} {Domains}},
     journal = {Canadian journal of mathematics},
     pages = {1024--1030},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-103-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-103-9/}
}
TY  - JOUR
AU  - Ohm, Jack
TI  - Primary Ideals in Prüfer Domains
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 1024
EP  - 1030
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-103-9/
DO  - 10.4153/CJM-1966-103-9
ID  - 10_4153_CJM_1966_103_9
ER  - 
%0 Journal Article
%A Ohm, Jack
%T Primary Ideals in Prüfer Domains
%J Canadian journal of mathematics
%D 1966
%P 1024-1030
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-103-9/
%R 10.4153/CJM-1966-103-9
%F 10_4153_CJM_1966_103_9

[1] 1. Bourbaki, N., Algèbre commutative, Chap. 7 (Paris, 1965). Google Scholar

[2] 2. Gilmer, R., The cancellation law for ideals in a commutative ring., Can. J. Math., 17 (1965), 281–287. Google Scholar

[3] 3. Gilmer, R. and Ohm, J., Primary ideals and valuation ideals, Trans. Amer. Math. Soc., 117 (1965), 237–250. Google Scholar

[4] 4. Krull, W., Idealtheorie in unendlichen algebraischen Zahlkörpern. Math. Z., 29 (1929), 42–54; II, loc. cit., 31 (1930), 527-557. Google Scholar

[5] 5. Krull, W., Beiträge zur Arithmetik kommutativer Integritätsbereiche, Math. Z., 41 (1936), 545–569. Google Scholar

[6] 6. Krull, W., Idealtheorie (New York, 1948). Google Scholar

[7] 7. Krull, W., Nagata, M., Local rings (New York, 1962). Google Scholar

[8] 8. Nakano, N., Unendliche algebraische Zahlkörper, J. Sci. Hiroshima Univ., (a) 15 (1952), 171–175; (b) 16 (1953), 425-439; (c) 17 (1953), 11-20; (d) 17 (1954), 321-343; (e) 18 (1954), 129-136; (f) 18 (1955), 257-269; (g) 18 (1955), 271-287; (h) 19 (1955), 239-253; (i) 19 (1956), 439-455; (j) 20 (1956), p. 47. Google Scholar

[9] 9. Schilling, O. F. G., The theory of valuations (Providence, 1950). Google Scholar

[10] 10. Zariski, O. and Samuel, P., Commutative algebra, Vol. 1 (Princeton, 1958). Google Scholar

[11] 11. Zariski, O. and Samuel, P., Commutative algebra, Vol. 2 (Princeton, 1960). Google Scholar

Cité par Sources :