Algebraic Theory

  • D. P. Parent
Part of the Problem Books in Mathematics book series (PBM)


Let L be a field; if K is a subfield of L we also say that L is an EXTENSION FIELD OF K. If L, as a vector space over K, has finite dimension n, we say that the extension L|K is a FINITE EXTENSION OF DEGREE n, and this is written n = [L:K]; otherwise we say that L|K is an INFINITE EXTENSION. If M|L and L|K are two finite extensions, M|K is then finite, and [M:K] = [M:L] x [L:K].


Prime Number Prime Ideal Galois Group Prime Divisor Algebraic Theory 
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© Springer Science+Business Media New York 1984

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