Chapter V

Commutative Fields

Except where the contrary is expressly stated, all the fields considered in this chapter are commutative; all algebras are associative and unital and the algebra homomorphisms are unital, every subalgebra of an algebra contains the unit element of that algebra. Whenever a field K is said to be contained in a ring L (in particular in a field) without further specification, it is understood that K is a subring of L; we shall also say that K is a subfield of L, or also (if L is a field) that L is an extension field of K.