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Explicit Brauer Induction is an important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this 1994 book it is derived algebraically, following a method of R. Boltje - thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to re-prove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous applications and this book is designed to introduce research algebraists to its possibilities. For example, the technique gives an improved construction of the Oliver-Taylor group-ring logarithm, which enables the author to study more effectively algebraic and number-theoretic questions connected with class-groups of rings.

Brauer groups. --- Representations of groups.

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This book offers a self-contained exposition of local class field theory, serving as a second course on Galois theory. It opens with a discussion of several fundamental topics in algebra, such as profinite groups, p-adic fields, semisimple algebras and their modules, and homological algebra with the example of group cohomology. The book culminates with the description of the abelian extensions of local number fields, as well as the celebrated Kronecker-Weber theory, in both the local and global cases. The material will find use across disciplines, including number theory, representation theory, algebraic geometry, and algebraic topology. Written for beginning graduate students and advanced undergraduates, this book can be used in the classroom or for independent study.

Class field theory --- Brauer groups --- Galois theory --- Galois cohomology

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Algebraic geometry --- Ordered algebraic structures --- Brauer groups --- Geometry, Algebraic --- Rings (Algebra) --- Brauer, Groupe de. --- Brauer groups. --- Geometrie algebrique --- Algebres et anneaux associatifs --- Cohomologie

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Class field theory --- Brauer groups --- Galois theory --- Galois cohomology --- Brauer groups. --- Class field theory. --- Galois cohomology. --- Galois theory. --- Brauer-Gruppe --- Galois-Kohomologie --- Galois-Theorie --- Lokale Klasse --- Théorie du corps de classes --- Groupes de Brauer --- Théorie de Galois --- Cohomologie galoisienne

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Brauer group --- Hopf algebras --- Galois theory --- Algèbres de Hopf --- Théorie de Galois --- Brauer groups. --- Algèbres de Hopf --- Théorie de Galois