Cyclic division algebras
Tóm tắt
A general example of cyclic division algebra is given, based on a construction of Brauer, yielding examples of division algebras of arbitrary prime exponent without proper central subalgebras, and also noncrossed products of arbitrary exponent.
Tài liệu tham khảo
A. A. Albert,Modern Higher Algebra, University of Chicago Press, Chicago, Illinois, 1937.
A. A. Albert,Structure of Algebras, Amer. Math. Soc. Colloq. Pub. 24, Providence, R.I., 1961.
S. A. Amitsur,On central division algebras, Israel J. Math.12 (1972), 408–422.
S. A. Amitsur and D. Saltman,Generic abelian crossed products, J. Algebra51 (1978), 76–87.
S. A. Amitsur, L. H. Rowen and J. P. Tignol,Division algebras of degree 4 and 8 with involution, Israel J. Math.33 (1979), 133–148.
R. Brauer,Uber den index und den exponenten von divisionsalgebren, Tohuko Math. J.37 (1933), 77–87.
A. Charnow,On the fixed field of a linear abelian group, J. London Math. Soc. (2),1 (1969), 348–350.
N. Jacobson,PI-algebras, an Introduction, Lecture Notes in Mathematics441, Springer Verlag, Berlin-Heidelberg-New York, 1975.
L. Risman,Cyclic algebras, complete fields, and crossed products, Israel J. Math.28 (1977), 113–128.
L. Rowen,On algebras with polynomial identity, Dissertation, Yale University, 1973.
L. Rowen,Identities in algebra with involution, Israel J. Math.20 (1975), 70–95.
L. Rowen,Central simple algebras, Israel J. Math.29 (1978), 285–301.
L. Rowen,Polynomial Identities in Ring Theory, Academic Press, New York, 1980.
L. Rowen,Division algebra counterexamples of degree 8, israel J. Math.38 (1981), 51–57.
D. Saltman,Noncrossed products of small exponent, Proc. Amer. Math. Soc.68 (1978), 165–168.
D. Saltman,Indecomposible division algebras, Comm. Alg.7 (1979), 791–817.
H. M. S. Wedderburn,On division algebras, Trans. Amer. Math. Soc.22 (1921), 129–135.
D. Winter,The Structure of Fields, Springer-Verlag, New York, Berlin, 1974.