Some properties of ring
Some properties [ edit ] Some basic properties of a ring follow immediately from the axioms: The additive identity is unique. The additive inverse of each element is unique. The multiplicative identity is unique. For any element x in a ring R , one has x 0 = 0 = 0 x (zero is an absorbing element with respect to multiplication) and (–1) x = – x . If 0 = 1 in a ring R (or more generally, 0 is a unit element), then R has only one element, and is called the zero ring . If a ring R contains the zero ring as a subring, then R itself is the zero ring. [6] The binomial formula holds for any x and y satisfying xy = yx . Example: Integers modulo 4 [ edit ] See also: Modular arithmetic Equip the set � / 4 � = { 0 ¯ , 1 ¯ , 2 ¯ , 3 ¯ } with the following operations: The sum � ¯ + � ¯ in...