Representation Theory - James Lingard
Representation Theory Representations Let G be a group and V a vector space over a field k.A representation of G on V is a group homomorphism ‰: G ! Aut(V).The degree (or dimension) of ‰ is just dimV.
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Galois Theory - James Lingard
www.jchl.co.ukDefinition A field extension L=K is algebraic if every fi 2 L is algebraic over K.It is pure transcen- dental if every fi 2 LnK is transcendental over K. 1.2 Classification of simple algebraic extensions Given a field K and an irreducible polynomial f 2 K[X], recall that the quotient ring K[X]=(f) is a field. Therefore we have a simple algebraic field extension K ,!
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