Algebraic field extensions: a continuation

We shall talk about the algebraic extension . We shall assume that both and are algebraic over the field . Assume . Hence, the basis for the vector space over is . Now say . Then the basis of over is . It is known that the basis of over is (arranged as a matrix).Continue reading “Algebraic field extensions: a continuation”

Field extensions…..things that books won’t explicitly point out.

This is going to flesh out some real details. First, something exceedingly important. When doing elementary algebra for the first time (say in grade 4), one often asks “what is ?” The answer to that is “” is just a useful construct that is temporarily holding place, waiting for an actual number to pop inContinue reading “Field extensions…..things that books won’t explicitly point out.”