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 
, 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.
