Cambridge University Press, 8 sept. 2005 - 202 pages
A classic advanced textbook, containing a cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject. The author gives an integrated presentation of overall theory and its applications in, for example, the study of groups of matrices, group representations, and in settling the problems of Burnside and Kurosh. Readers are also informed of open questions. Definitions are kept to a minimum and the statements of the theorems are sharp and clear.
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The Jacobson Radical
Representations of Finite Groups
The GolodShafarevitch Theorem
algebra over F algebraic algebra algebraic integer Amer Artinian ring ascending chain condition Burnside problem central division algebra central simple algebra characteristic roots commuting ring condition on left conjugate classes contains Corollary define Definition dimensional over F direct sum division algebra division ring equivalent factor set field F finite group finite-dimensional Galois group Goldie ring hence homomorphic image idempotent irreducible i?-module irreducible representation isomorphic left annihilators left ideal Let F linear transformations linearly independent mapping Math maximal regular right maximal subfield minimal right ideal nil ideals nilpotent ideals P.I. algebras polynomial identity primitive ring Proof radical regular right ideal representation of G result ring of linear ring satisfying ring theory roots of unity satisfies a polynomial semisimple Artinian ring semisimple ring simple Artinian ring simple ring subalgebra subdirect sum subring Suppose torsion group two-sided ideal unit element vector space Wedderburn's theorem yields zero divisor