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[Invertible Element] [2005-11-20]
iamet 发表在 ∑〖数学〗
| 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.
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学好数理化，走遍天下都不怕！ | |
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