Bulletin of the American Mathematical Society

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Book Information:

Author: John Dauns
Title: A concrete approach to division rings
Additional book information: Research and Education in Mathematics, Vol. 2, Heldermann, Verlag, Berlin, 1982, xx + 417 pp., $78.00. ISBN 3-8853-8202-4.

Author: P. X. Draxl
Title: Skew fields
Additional book information: London Mathematical Society Lecture Note Series 81, Cambridge University Press, New York, 1982, 182 pp., $19.95. ISBN 0-5212-7274-2.

S. A. Amitsur, L. H. Rowen, and J.-P. Tignol, Division algebras of degree $4$ and $8$ with involution, Israel J. Math. 33 (1979), no. 2, 133–148. MR 571249, DOI 10.1007/BF02760554

S. A. Amitsur and D. Saltman, Generic Abelian crossed products and $p$-algebras, J. Algebra 51 (1978), no. 1, 76–87. MR 491789, DOI 10.1016/0021-8693(78)90136-9

M. Artin, Brauer-Severi varieties, Brauer groups in ring theory and algebraic geometry (Wilrijk, 1981), Lecture Notes in Math., vol. 917, Springer, Berlin-New York, 1982, pp. 194–210. MR 657430

B. Fein and M. Schacher, Brauer groups of rational function fields over global fields, The Brauer group (Sem., Les Plans-sur-Bex, 1980) Lecture Notes in Math., vol. 844, Springer, Berlin, 1981, pp. 46–74. MR 611865

Edward Formanek, The center of the ring of $4\times 4$ generic matrices, J. Algebra 62 (1980), no. 2, 304–319. MR 563230, DOI 10.1016/0021-8693(80)90184-2

Nathan Jacobson, $\textrm {PI}$-algebras, Lecture Notes in Mathematics, Vol. 441, Springer-Verlag, Berlin-New York, 1975. An introduction. MR 0369421

[MS] A. S. Merkuriev and A. A. Suslin, K cohomology of Severi Brauer varieties and norm residue homeomorphism, preprint, 1981.

A. S. Merkurjev, Brauer groups of fields, Comm. Algebra 11 (1983), no. 22, 2611–2624. MR 733345, DOI 10.1080/00927878308822983

[M2] A. S. Merkuriev, The Brauer group of fields, preprint, 1982.

John Milnor, Introduction to algebraic $K$-theory, Annals of Mathematics Studies, No. 72, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1971. MR 0349811

Claudio Procesi, Rings with polynomial identities, Pure and Applied Mathematics, vol. 17, Marcel Dekker, Inc., New York, 1973. MR 0366968

Lawrence J. Risman, Cyclic algebras, complete fields, and crossed products, Israel J. Math. 28 (1977), no. 1-2, 113–128. MR 457412, DOI 10.1007/BF02759787

Louis Halle Rowen, Cyclic division algebras, Israel J. Math. 41 (1982), no. 3, 213–234. MR 657857, DOI 10.1007/BF02771722

Louis Halle Rowen, Polynomial identities in ring theory, Pure and Applied Mathematics, vol. 84, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. MR 576061

Louis H. Rowen and David J. Saltman, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 84 (1982), no. 2, 162–164. MR 637160, DOI 10.1090/S0002-9939-1982-0637160-2

David J. Saltman, Noncrossed product $p$-algebras and Galois $p$-extensions, J. Algebra 52 (1978), no. 2, 302–314. MR 480640, DOI 10.1016/0021-8693(78)90240-5

David J. Saltman, Noncrossed products of small exponent, Proc. Amer. Math. Soc. 68 (1978), no. 2, 165–168. MR 476794, DOI 10.1090/S0002-9939-1978-0476794-4

David J. Saltman, Retract rational fields and cyclic Galois extensions, Israel J. Math. 47 (1984), no. 2-3, 165–215. MR 738167, DOI 10.1007/BF02760515

Winfried Scharlau, Zur Existenz von Involutionen auf einfachen Algebren, Math. Z. 145 (1975), no. 1, 29–32 (German). MR 393115, DOI 10.1007/BF01214495

[ART] S. A. Amitsur, L. Rowen and J. P. Tignol, Division algebras degree 4 and 8 with involution, Israel J. Math. 33 (1979), 133-148. MR 0571249




[AS] S. A. Amitsur and D. Saltman, Generic abelian crossed products and p-algebras, J. Algebra 51 (1978), 76-87. MR 491789




[A] M. Artin, Brauer-Severi varieties, Brauer Groups in Ring Theory and Algebraic Geometry (Oystaeyen and Vershoren, eds.), Lecture Notes in Math., vol. 917, Springer-Verlag, 1982. MR 657430




[FS] B. Fein and M. Schacher, Brauer groups of rational function fields over global fields, Le Groupe de Brauer (M. Kervaire, ed.), Lecture Notes in Math., vol. 844, Springer-Verlag, New York, 1981. MR 611865




[F] E. Formanek, The center of the ring of 4 X 4 generic matrices, J. Algebra 62 (1980), 304-320. MR 563230




[J] N. Jacobson, P. I. algebras, Lecture Notes in Math., vol. 441, Springer-Verlag, 1975. MR 369421




[MS] A. S. Merkuriev and A. A. Suslin, K cohomology of Severi Brauer varieties and norm residue homeomorphism, preprint, 1981.




[M1] A. S. Merkuriev, On Brauer groups of fields, preprint 1983. MR 733345




[M2] A. S. Merkuriev, The Brauer group of fields, preprint, 1982.




[Mi] J. Milnor, Algebraic K-theory, Princeton Univ. Press, Princeton, N. J., 1971. MR 349811




[P] C. Procesi, Rings with polynomial identity, Dekker, New York, 1973. MR 366968




[Ri] L. Risman, Cyclic algebras, complete fields, and crossed products, Israel J. Math. 28, 113-128. MR 457412




[Rl] L. Rowen, Cyclic division algebras, Israel J. Math. 41 (1982), 213-234. MR 657857




[R2] L. Rowen, Polynomial identities in ring theory, Academic Press, 1980. MR 576061




[RS] L. H. Rowen and D. Saltman, Dihedral algebras are cyclic, Proc. Amer. Math. Soc. 84 (1982). MR 637160




[S1] D. Saltman, Noncrossed product p algebras and Galois p extensions, J. Algebra 52 (1978), 302-314. MR 480640




[S2] D. Saltman, Noncrossed products of small exponent, Proc. Amer. Math. Soc. 68 (1978), 165-168. MR 476794




[S3] D. Saltman, Retract rational fields and cyclic Galois extensions, Israel J. Math. (to appear). MR 738167




[Sc] W. Scharlau, Zur existence von Involutionen auf einfachen Algebren, Math. Z. 145 (1975), 29-32. MR 393115