Fun with polynomials and linear algebra; or, slight abstract nonsense

Fun with polynomials and linear algebra; or, slight abstract nonsense Posted This is mostly a bunch of notes to myself (with some slight expansion) and is a combination/extension/simplification of theorems/ideas/constructions from a bunch of texts, including Wistbauer’s “Foundations of Module and Ring Theory” and Fuhrmann’s “A Polynomial Approach to Linear Algebra”, along with others that at this point I don’t recall. While most of the things here are pretty standard (indeed, many of these are..