ringname1 http://www.openmath.org/cd/ringname1.ocd 2005-04-01 2004-03-08 1 0 experimental alg1 arith1 fns1 fns2 group1 group2 logic1 monoid1 monoid2 nums1 quant1 relation1 set1 setname1 ring1 A CD of names of frequently used rings in ring theory. Written by Arjeh M. Cohen 2004-03-08 Z This symbol represents the ring of integers. The integer 1 is the identity element of this ring. 1 The carrier set of this ring is the set of integers. quaternions This symbol represents a unary function. Its argument is a ring R. When evaluated on R, the function represents the ring of quaternions over R, that is, the ring with basis 1,i,j,k over R such that ij=-ji=k, i^2=j^2=k^2=-1. The quaternion ring over R is isomorphic to the quotient of the free ring over R generated by i, j, k subject to the relations ij=-ji=k and i^2=j^2=k^2=-1. 2 1 2 1 2 1 Zm application This symbol represents the ring of integers modulo m, where m is not necessarily a prime. It takes one argument, the integer m. The ring of integers mod 12: 12