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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 just slightly generalized definitions given in introductions to linear algebra over arbitrary fields!) there is some stuff here that might be weird and surprising unless you’re already quite well-versed in the language of module theory.
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