## Noncrossed products over $k_{\mathfrak {p}}(t)$

HTML articles powered by AMS MathViewer

- by Eric S. Brussel PDF
- Trans. Amer. Math. Soc.
**353**(2001), 2115-2129 Request permission

## Abstract:

Noncrossed product division algebras are constructed over rational function fields $k(t)$ over number fields $k$ by lifting from arithmetic completions $k(t)_{\mathfrak {p}}$. The existence of noncrossed products over $\mathfrak {p}$-adic rational function fields $k_{\mathfrak {p}}(t)$ is proved as a corollary.## References

- S. A. Amitsur,
*On central division algebras*, Israel J. Math.**12**(1972), 408β420. MR**318216**, DOI 10.1007/BF02764632 - S. A. Amitsur and D. Saltman,
*Generic Abelian crossed products and $p$-algebras*, J. Algebra**51**(1978), no.Β 1, 76β87. MR**491789**, DOI 10.1016/0021-8693(78)90136-9 - JΓ³n Kr. Arason, Burton Fein, Murray Schacher, and Jack Sonn,
*Cyclic extensions of $K(\sqrt {-1})/K$*, Trans. Amer. Math. Soc.**313**(1989), no.Β 2, 843β851. MR**929665**, DOI 10.1090/S0002-9947-1989-0929665-2 - Artin, E., Tate, J.:
*Class Field Theory*, Addison-Wesley, Reading, Mass., 1967. - Kenneth S. Brown,
*Cohomology of groups*, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York-Berlin, 1982. MR**672956** - Eric Brussel,
*Noncrossed products and nonabelian crossed products over $\mathbf Q(t)$ and $\mathbf Q((t))$*, Amer. J. Math.**117**(1995), no.Β 2, 377β393. MR**1323680**, DOI 10.2307/2374919 - J. W. S. Cassels and A. FrΓΆhlich (eds.),
*Algebraic number theory*, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. Reprint of the 1967 original. MR**911121** - Burton Fein, David J. Saltman, and Murray Schacher,
*Brauer-Hilbertian fields*, Trans. Amer. Math. Soc.**334**(1992), no.Β 2, 915β928. MR**1075382**, DOI 10.1090/S0002-9947-1992-1075382-0 - Bill Jacob and Adrian Wadsworth,
*Division algebras over Henselian fields*, J. Algebra**128**(1990), no.Β 1, 126β179. MR**1031915**, DOI 10.1016/0021-8693(90)90047-R - Nathan Jacobson,
*Finite-dimensional division algebras over fields*, Springer-Verlag, Berlin, 1996. MR**1439248**, DOI 10.1007/978-3-642-02429-0 - I. Reiner,
*Maximal orders*, London Mathematical Society Monographs, No. 5, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1975. MR**0393100** - David J. Saltman,
*Generic Galois extensions and problems in field theory*, Adv. in Math.**43**(1982), no.Β 3, 250β283. MR**648801**, DOI 10.1016/0001-8708(82)90036-6 - David J. Saltman,
*Division algebras over $p$-adic curves*, J. Ramanujan Math. Soc.**12**(1997), no.Β 1, 25β47. MR**1462850** - C. J. Everett Jr.,
*Annihilator ideals and representation iteration for abstract rings*, Duke Math. J.**5**(1939), 623β627. MR**13** - Jean-Pierre Serre,
*Local fields*, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, New York-Berlin, 1979. Translated from the French by Marvin Jay Greenberg. MR**554237**

## Additional Information

**Eric S. Brussel**- Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
- Email: brussel@mathcs.emory.edu
- Received by editor(s): December 8, 1998
- Received by editor(s) in revised form: September 13, 1999
- Published electronically: November 21, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**353**(2001), 2115-2129 - MSC (2000): Primary 16K20; Secondary 11R37
- DOI: https://doi.org/10.1090/S0002-9947-00-02626-X
- MathSciNet review: 1813610