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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.

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Why is $(\mathbb{Z}/3\mathbb{Z})^3$ not a class group of an imaginary quadratic number field ?

The only proof that I know that $(\mathbb{Z}/3\mathbb{Z})^3$ does not appear as the class group of a quadratic imaginary number field is by brute force search. Roughly, the idea is that since class n …
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5 votes

Does category theory help understanding abstract algebra?

Sounds like you might want to petition for an exception to the prerequisites. I don't think Lang's Abstract Algebra is probably your best bet (stick to something decidedly undergraduate -- maybe Gall …
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