Mathematics - Abstract Algebra - Rings and fields - From Groups to Rings to Fields

10 steps: (1) A RING (R,+,×) has two operations. (R,+) is an abelian group, × is associative and distributes over +. (2) Example: (ℤ,+,×). Addition forms a group, multiplication is associative and distributive. (3) Commutative ring: a×b=b×a. Ring with unity: has multiplicative identity 1. (4) Exampl