Brauer type embedding problems.QA247 2005-042813 0-8218-3726-5 Brauer type embedding problems In Galois theory, a branch of mathematics, the embedding problem is a generalization of the inverse Galois problem. Roughly speaking, it asks whether a given Galois extension can be embedded into a Galois extension in such a way that the restriction map between the corresponding . Ledet, Arne. (Fields Institute The Fields Institute for Research in Mathematical Sciences is located on the University of Toronto campus in Toronto, Ontario, Canada, although the institute's first home was at the University of Waterloo, where it was founded in 1992. monographs; 21) Amer. Mathematical Society, [c]2005 171 p. $52.00 Ledet examines Brauer embedding problems, and related embedding problem types, primarily where pi has prime order, bringing together Galois theory Ga·lois theory n. The part of algebra concerned with the relation between solutions of a polynomial equation and the fields containing those solutions. , Brauer group In mathematics, the Brauer group arose out of an attempt to classify division algebras over a given field K. It is an abelian group with elements isomorphism classes of division algebras over K, such that the center is exactly K. theory, group cohomology In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors H n. , and the theory of quadratic forms, all of which are covered in the text. He begins with a review of Galois theory, followed by a descriptions of inverse Galois theory and embedding problems, Brauer groups, including basic facts about their algebra, group cohomology, quadratic forms, the process of decomposing obstructions, working quadratic forms and embedding problems, and reducing the embedding problem. Ledet also includes an examination of pro-finite Galois theory. Ledet includes exercises throughout. Readers should have a background in classical Galois theory and the attendant algebra. |
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