name: rings description: "Problem-solving strategies for rings in abstract algebra" allowed-tools: [Bash, Read]
Rings
When to Use
Use this skill when working on rings problems in abstract algebra.
Decision Tree
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Is R a ring?
- (R, +) is an abelian group
- Multiplication is associative
- Distributive laws: a(b+c) = ab + ac and (a+b)c = ac + bc
z3_solve.py prove "ring_axioms"
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Ring Properties
- Commutative ring: ab = ba for all a, b?
- Ring with unity: exists 1 such that 1a = a1 = a?