[Invertible Element] - 达人(其实～我是卧底，来自外星)

2005/11/20 | [Invertible Element]
类别(∑〖数学〗) | 评论(0) | 阅读(37) | 发表于 12:41: An element admitting a multiplicative or additive inverse. In most cases, the choice between these two options is clear from the context, as, for example, in a monoid, where there is only one operation available.

Ambiguity could arise in a unit ring, where both an addition and a multiplication are defined. In such cases, the convention is to refer the word invertible only to multiplication. This is reasonable since, with respect to addition, a ring is a group, so that every element is invertible. With respect to multiplication, however, many different situations can occur. The zero element is never invertible, the element 1 is always invertible and inverse to itself. In the ring , the only invertible elements are 1 and -1, whereas in , every nonzero element is invertible (since this is precisely the property that defines a field).

The invertible elements of a unit ring are also called units.; 0