|
On the intersection property of Dubrovin valuation rings
Author(s):
Zhao
Yicai
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2825-2830.
MSC (1991):
Primary 16A40, 16A10
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
It is shown that of the three axioms Gräter specified for his intersection property of Dubrovin valuation rings in central-simple algebras, the second and third axioms actually follow from the first.
References:
- [AD]
- J. H. Alajbegovic and N. I. Dubrovin, Noncommutative Prüfer rings, J. Algebra 135 (1990), 165-176. MR 92b:16019
- [AS]
- S. A. Amitsur and L. W. Small, Prime ideals in PI-rings, J. Algebra 62 (1980), 358-383. MR 81c:16027
- [D1]
- N. I. Dubrovin, Noncommutative valuation rings, Trudy Moskov. Mat. Obshch. 45 (1982), 265-280; English transl. in Trans. Moscow Math. Soc. 45 (1984), 273-287. MR 85d:16002
- [D2]
- N. I. Dubrovin, Noncommutative valuation rings in simple finite-dimensional algebra over a field, Mat. Sb. 123 (165) (1984), 496-509; English transl. in Math. USSR Sb. 51 (1985), 493-505. MR 85j:16020
- [E]
- O. Endler, Valuation Theory, Springer-Verlag, New York, 1972. MR 50:9847
- [G1]
- J. Gräter, The Defektsatz for central simple algebras, Trans. Amer. Math. Soc. 330 (1992), 823-843. MR 92f:16018
- [G2]
- J. Gräter, Prime PI-rings in which finitely generated right ideals are principal, Forum Math. 4 (1992), 447-463. MR 93i:16026
- [K]
- I. Kaplansky, Commutative Rings, The Univ. of Chicago Press 1970. MR 49:10674
- [M1]
- P. J. Morandi, An approximation theorem for Dubrovin valuation rings, Math. Zeit. 207 (1991), 71-82. MR 92g:16021
- [M2]
- P. J. Morandi, Maximal orders over valuation rings, J. Algebra 152 (1992), 313-341. MR 93k:16028
- [M3]
- P. J. Morandi, Noncommutative Prüfer rings satisfying a polynomial identity, J. Algebra 161 (1993), 324-341. MR 94k:16019
- [R]
- J. C. Robson, Rings in which finitely generated right ideals are principal, Proc. London Math. Soc. 17 (1967), 617-628. MR 36:200
- [W]
- A. R. Wadsworth, Dubrovin valuation rings and Henselization, Math. Ann. 283 (1989), 301-328. MR 90f:16009
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
16A40, 16A10
Retrieve articles in all Journals with MSC
(1991):
16A40, 16A10
Additional Information:
Zhao
Yicai
Affiliation:
Institute of Mathematics, Fudan University, Shanghai 200433, People's Republic of China
DOI:
10.1090/S0002-9939-97-03987-7
PII:
S 0002-9939(97)03987-7
Received by editor(s):
December 18, 1995
Received by editor(s) in revised form:
March 29, 1996
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1997,
American Mathematical Society
|