Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google