Merge pull request twitter#339 from twitter/addCommentSemiring

Add a commment to close 334

algebird-core/src/main/scala/com/twitter/algebird/Ring.scala

@@ -24,6 +24,21 @@ import scala.annotation.implicitNotFound
  *  - additive identity aka zero
  *  - addition
  *  - multiplication
+ *
+ *
+ *  Note, if you have distributive property, additive inverses, and multiplicative identity you
+ *  can prove you have a commutative group under the ring:
+ *
+ *  1. (a + 1)*(b + 1) = a(b + 1) + (b + 1)
+ *  2.                 = ab + a + b + 1
+ *  3. or:
+ *  4.
+ *  5.                 = (a + 1)b + (a + 1)
+ *  6.                 = ab + b + a + 1
+ *  7.
+ *  8. So: ab + a + b + 1 == ab + b + a + 1
+ *  9.   using the fact that -(ab) and -1 exist, we get:
+ * 10. a + b == b + a
  */
 
 @implicitNotFound(msg = "Cannot find Ring type class for ${T}")