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Elements of General Representation Theory 1
Extension of the GroundField
33 other sections not shown
9l-module A-module Abelian group absolutely indecomposable absolutely irreducible algebraically closed field associative algebra automorphism bilinear form char commutative completely reducible composition factor conjugate contradiction cyclic defined denote dimK dimKV direct sum direct summand divides elementary Abelian epimorphism exists exponent Fermat prime field of characteristic finite dimension finite group follows at once free associative algebra free group GF(p group-ring Hence HomKffi(V homomorphism ideal of g idempotents indecomposable projective inductive hypothesis irreducible Kİ-module isomorphic K-basis Kİ-submodule Lemma Lie algebra Lie ring linear transformation linearly independent matrix maximal minimal normal subgroup minimum polynomial monomorphism multiplicity nilpotent non-singular non-zero operates trivially p-group p-length p-soluble permutes projective Kİ-module Proof proved by induction right ideals soluble group spanned splitting field subalgebra submodule subspace Suppose that 91 Sylow p-subgroup symplectic Theorem transversal vector space