Geodesic
A Note on Quotient Fields of Power Series Rings
Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 162-164

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

Let R be an integral domain with quotient field K. If R has an overling S ≠ K, such that S[X] is integrally closed, then the "algebraic degree" of K((X)) over the quotient field of R[X] is infinite. In particular, it holds for completely integrally closed domain or Noetherian domain R.
DOI : 10.4153/CMB-1994-023-7
Mots-clés : 13F25, 12F05, 13B22, power series ring, quotient field, algebraic degree, completely integrally closed, Noetherian 
Chu, Huah; Lang, Yi-Chuan. A Note on Quotient Fields of Power Series Rings. Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 162-164. doi: 10.4153/CMB-1994-023-7
@article{10_4153_CMB_1994_023_7,
     author = {Chu, Huah and Lang, Yi-Chuan},
     title = {A {Note} on {Quotient} {Fields} of {Power} {Series} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {162--164},
     year = {1994},
     volume = {37},
     number = {2},
     doi = {10.4153/CMB-1994-023-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-023-7/}
}
TY  - JOUR
AU  - Chu, Huah
AU  - Lang, Yi-Chuan
TI  - A Note on Quotient Fields of Power Series Rings
JO  - Canadian mathematical bulletin
PY  - 1994
SP  - 162
EP  - 164
VL  - 37
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-023-7/
DO  - 10.4153/CMB-1994-023-7
ID  - 10_4153_CMB_1994_023_7
ER  - 
%0 Journal Article
%A Chu, Huah
%A Lang, Yi-Chuan
%T A Note on Quotient Fields of Power Series Rings
%J Canadian mathematical bulletin
%D 1994
%P 162-164
%V 37
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-023-7/
%R 10.4153/CMB-1994-023-7
%F 10_4153_CMB_1994_023_7

[1] 1. Bourbaki, N., Elements of Mathematics, Commutative Algebra, Addison Wesley, 1972. Google Scholar

[2] 2. Gilmer, R., A Note on the quotient field of the domain D[[X]], Proc. Amer. Math. Soc. 18(1967), 1138–1140. Google Scholar

[3] 3. Nagata, M., Local Rings, Interscience Publishers, 1962. Google Scholar

[4] 4. Ohm, J., Some counterexamples related to integral closure in D[[X]], Trans. Amer. Math. Soc. 122(1966), 321–333. Google Scholar

[5] 5. Sheldon, P. B., How changing D[[X]] changes its quotient field, Trans. Amer. Math. Soc. 159(1971), 223– 244. Google Scholar

[6] 6. Zariski, O. and Samuel, P., Commutative algebra, Vol. I, Van Nostrand, New York, 1958. Google Scholar

Cité par Sources :