Rings

When to Use

Use this skill when working on rings problems in abstract algebra.

Decision Tree

1. 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"

2. Ring Properties

   • Commutative ring: ab = ba for all a, b?
   • Ring with unity: exists 1 such that 1a = a1 = a?
   • Integral domain: ab = 0 implies a = 0 or b = 0?