\(\DeclareMathOperator{\ann}{ann} \DeclareMathOperator{\Ass}{Ass} \DeclareMathOperator{\Aut}{Aut} \DeclareMathOperator{\can}{can} \DeclareMathOperator{\Ch}{Ch} \DeclareMathOperator{\char}{char} \DeclareMathOperator{\cp}{CharPoly} \DeclareMathOperator{\codim}{codim} \DeclareMathOperator{\coker}{coker} \DeclareMathOperator{\colim}{colim} \DeclareMathOperator{\cone}{cone} \DeclareMathOperator{\cont}{cont} \DeclareMathOperator{\diam}{diam} \DeclareMathOperator{\dim}{dim} \DeclareMathOperator{\edim}{embdim} \DeclareMathOperator{\End}{End} \DeclareMathOperator{\eval}{eval} \DeclareMathOperator{\Ext}{Ext} \DeclareMathOperator{\Frac}{Frac} \DeclareMathOperator{\Fun}{Fun} \DeclareMathOperator{\Gal}{Gal} \DeclareMathOperator{\gcd}{gcd} \DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\height}{height} \DeclareMathOperator{\Hom}{Hom} \DeclareMathOperator{\id}{id} \DeclareMathOperator{\im}{im} \DeclareMathOperator{\Inn}{Inn} \DeclareMathOperator{\ker}{ker} \DeclareMathOperator{\lcm}{lcm} 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Preface The Structure of this Text

Additions.

Solvable Groups: Justification pending
Group Rings: Used to rigorously define polynomial rings, used in many advanced forms of mathematics, such as representation theory, (co)homology, etc
Noetherian Rings: Better to include in the ring section, since we’ll need them when we classify finitely generated modules in PIDs anyway. Since much of commutative algebra is based in noetherian rings, the earlier the exposure the better.
Localization: Justification pending
Algebras: Justification pending

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