Abstract Algebra
These pages consist of my notes on various things that are broadly “algebra”. A few conventions to keep in mind:
[example] [extitle]$\NN$ convention.[/extitle] The natural numbers $\NN$ refers to the set consisting of the numbers
\[\begin{align*} 0, \quad 1, \quad 2, \quad 3, \quad\ldots. \end{align*}\][/example]
[example] [extitle]Unital ring convention.[/extitle] Whenever I say the word “ring”, I always mean a unital ring. Whenever I refer to a non-unital ring, I will say rng. [/example]
[example] [extitle]Commutative ring convention.[/extitle] My interests are primarily in non-commutative algebra. Accordingly, on these pages, I do NOT assume that the rings are commutative unless I explicitly say so somewhere on the page. [/example]
I am also a strong proponent of the rings-before-groups exposition. Accordingly, I deliberately place my notes on rings before my notes on groups and I also prove things in my groups section using ring theory.