Ring Theory
Rings A ring is a non empty set R with two binary operations called addition and multiplication, respectively satisfying Axiom 1. Closure x, y R x y R Axiom 2. Commutative For every x, y R x y y x Axiom 3. Associative x, y, z R x (y z) (x y) z Axiom 4. Neutral th R such that x R, x th th x x We denote th by 0 Axiom 5. Inverse a R the equation a+ x th has a solution. Note that (R is an Abelian group. Axiom 6. Closure x, y R x y R Axiom 7. Associative x, y, z R, x (y z) (x y) z Axiom 8. Ditributive