Geodesic
Localizations of H i and D i Rings
Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 815-819

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

In this paper we study conditions under which certain localizations of semilocal H i and D i rings satisfy the second chain condition. Two of these results are as follows. 1) If P is a prime in a semilocal Hi ring with depth P > i ≧ height P — 1, then RP satisfies the second chain condition. 2) If P is a prime in a semilocal Dt ring with depth P ≧ i, then RP satisfies the second chain condition. 
Houston, Evan G. Localizations of H i and D i Rings. Canadian journal of mathematics, Tome 28 (1976) no. 4, pp. 815-819. doi: 10.4153/CJM-1976-078-5
@article{10_4153_CJM_1976_078_5,
     author = {Houston, Evan G.},
     title = {Localizations of {H} i and {D} i {Rings}},
     journal = {Canadian journal of mathematics},
     pages = {815--819},
     year = {1976},
     volume = {28},
     number = {4},
     doi = {10.4153/CJM-1976-078-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-078-5/}
}
TY  - JOUR
AU  - Houston, Evan G.
TI  - Localizations of H i and D i Rings
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 815
EP  - 819
VL  - 28
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-078-5/
DO  - 10.4153/CJM-1976-078-5
ID  - 10_4153_CJM_1976_078_5
ER  - 
%0 Journal Article
%A Houston, Evan G.
%T Localizations of H i and D i Rings
%J Canadian journal of mathematics
%D 1976
%P 815-819
%V 28
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-078-5/
%R 10.4153/CJM-1976-078-5
%F 10_4153_CJM_1976_078_5

[1] 1. Houston, E. G. and McAdam, S., Chains of primes in noeiherian rings, Indiana University Math. J. 24 (1975), 741–753. Google Scholar

[2] 2. Kaplansky, I., Commutative rings (Allyn and Bacon, Boston, 1970). Google Scholar

[3] 3. McAdam, S., Saturated chains in noetherian rings, Indiana Univ. Math. J. 23 (1974), 719–728. Google Scholar

[4] 4. McAdam, S. and Ratliff, L. J., Jr., Semi-local taut rings, manuscript. Google Scholar

[5] 5. McAdam, S. and Ratliff, L. J., Jr., Polynomial rings and Hi-local rings (II), manuscript. Google Scholar

[6] 6. Pettit, M. E., Properties of Hi-rings, Ph.D. Thesis, Univ. of California at Riverside, 1973. Google Scholar

[7] 7. Ratliff, L. J., Jr., On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals (I), Amer. J. Math. 01 (1969), 508–528. Google Scholar

[8] 8. Ratliff, L. J., Jr., Characterizations of catenary rings, Amer. J. Math. 1)3 (1971), 1070–1108. Google Scholar

Cité par Sources :