Algebra II

Algebra II is a graduate course on the structure theory of rings and modules, the framework that turns "ring elements acting on something" into a precise classification of what those somethings can look like. You'll work through proof-based problem sets and quizzes building up to the Artin-Wedderburn classification of semisimple algebras, the Krull-Schmidt decomposition of indecomposables, and Maschke's theorem on group algebras, plus a presentation component where you talk through a result yourself. It picks up where a first algebra course leaves off and is the language you'll need for representation theory, homological algebra, and algebraic number theory downstream.