x1 is the one(-like) element/multiplicative identity of structure/ring x2; often is denoted by ' 1R ' or ' IR ' or by (when context is obvious) '1' or 'I', for structure/ring R (given by x2).
Definition and rules may be specified in the second terbri; this definition does not suppose that the ring is not the 0-ring (the trivial ring) with the mapping of all multiplications to 0 (in which case, the additive identity is also the multiplicative identity). The usage of "additive" and "multiplicative" in this context are defined by the ring. The n×n identity matrix over a given ring is an example of one such element. See also: nonsmi