Algebra: Abstract and Modern

11

Polynomial Rings

11.1 Rings of Polynomials

11.2 The Division Algorithm

11.3 Polynomials over a Field

11.4 Irreducible Polynomials

We are very familiar with polynomials which are introduced to us very early in our mathematical education, in fact, in high school itself, we are thoroughly drilled in adding, multiplying, dividing, factoring and simplifying them. We have learnt the remainder theorem in eighth or ninth standard. Later, at higher level, polynomials appear as functions and we were concerned with their continuity, derivatives and integrals and their maxima and minima. Now, we are interested in polynomials, but from neither of the above view points. Here, polynomials will simply be elements of a certain ring and we shall be concerned ...