|
Semiprime crossed products over copointed Hopf algebras
Author(s):
Declan
Quinn;
Serban
Raianu
Journal:
Proc. Amer. Math. Soc.
131
(2003),
29-33.
MSC (2000):
Primary 16W30
Posted:
July 15, 2002
MathSciNet review:
1929019
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove a result on the transfer of essentiality of extensions of modules over subnormalizing extensions of rings, then apply it to look at the semiprimeness of Hopf-Galois extensions, in particular that of crossed products.
References:
-
- 1.
- J. Bergen, S. Montgomery, Ideals and quotients in crossed products of Hopf Algebras, J. Algebra 152 (1992), 374-439. MR 94a:16054
- 2.
- R.J. Blattner, S. Montgomery, Crossed products and Galois extension of Hopf algebras, Pacific J. Math. 137 (1989), 37-54. MR 90a:16007
- 3.
- W. Chin, Crossed products of semisimple cocommutative Hopf algebras, Proc. AMS 116 (1992), 321-327. MR 92m:16059
- 4.
- W. Chin, D. Quinn, Rings graded by polycyclic-by-finite groups, Proc. AMS 102 (1988), 235-241. MR 89a:16001
- 5.
- M. Cohen, D. Fischman, S. Montgomery, Hopf Galois extensions, smash products, and Morita equivalence, J. Algebra 133 (1990), 351-372. MR 91i:16068
- 6.
- M. Cohen, S. Montgomery, Group-graded rings, smash products, and group actions, Trans. AMS 282 (1984), 237-258. MR 85i:16002
- 7.
- M. Cohen, S. Raianu, S. Westreich, Semi-invariants for Hopf algebra actions, Israel J. Math. 88 (1994), 279-306. MR 95j:16042
- 8.
- S. Dascalescu, C. Nastasescu, S. Raianu, Hopf Algebras: an Introduction, Pure and Applied Mathematics, A series of Monographs and Textbooks, vol. 235, Marcel Dekker Inc., New York-Basel, 2001. MR 2001j:16056
- 9.
- J.W. Fisher, S. Montgomery, Semiprime skew group rings, J. Algebra 52 (1978), 241-247. MR 58:772
- 10.
- T.Y. Lam, Lectures on Modules and Rings, GTM 189, Springer, 1999. MR 99i:16001
- 11.
- B. Lemonnier, Dimension de Krull et dualité de Morita dans les extensions triangulaires, Comm. Algebra 12 (1984), 3071-3110. MR 86g:16034
- 12.
- S. Montgomery, Hopf algebras and their actions on rings, CBMS Reg. Conf. Series 82, Providence, R.I., 1993. MR 94i:16019
- 13.
- S. Montgomery, H.-J. Schneider, Prime ideals in Hopf Galois extensions, Israel J. Math. 112 (1999), 187-235. MR 2001e:16075
- 14.
- C. Nastasescu, F. Van Oystaeyen, Graded ring theory, Math. Library 82, North Holland, 1982. MR 84i:16002
- 15.
- D. Passman, It's essentially Maschke's theorem, Rocky Mountain J. Math. 13 (1983), 37-54. MR 84e:16023
- 16.
- D. Quinn, Group-graded rings and duality, Trans. AMS 292 (1985), 155-167. MR 87d:16002
- 17.
- H.-J. Schneider, On inner actions of Hopf algebras and stabilizers of representations, J. Algebra 165 (1994), 138-163. MR 95d:16055
- 18.
- E.A. Whelan, Finite subnormalizing extensions of rings, J. Algebra 101 (1986), 418-432. MR 88e:16042
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
16W30
Retrieve articles in all Journals with
MSC (2000):
16W30
Additional Information:
Declan
Quinn
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
dpquinn@syr.edu
Serban
Raianu
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Address at time of publication:
Department of Mathematics, California State University Dominguez Hills, 1000 E Victoria Street, Carson, California 90747
Email:
sraianu@syr.edu, sraianu@csudh.edu
DOI:
10.1090/S0002-9939-02-06516-4
PII:
S 0002-9939(02)06516-4
Received by editor(s):
May 23, 2001
Received by editor(s) in revised form:
August 8, 2001
Posted:
July 15, 2002
Additional Notes:
The second author is on leave from University of Bucharest, Faculty of Mathematics
Communicated by:
Matin Lorenz
Copyright of article:
Copyright
2002,
American Mathematical Society
|