# Relationship between operations of a ring

Is there any requirement that the two operations of a ring have to be related to each other, excluding the requirement of distributivity? We all know from grade school that multiplication of integers is repeated addition, and we also know that the integers form a ring under addition and multiplication. Are there any other examples of rings whose second operation is based off of and/or defined in terms of the first, or are the integers basically the only example of that?

• The integers modulo $m$ come close. – André Nicolas Feb 4 '16 at 19:09