Unital ring axiom

Axiom asserting existence of a multiplicative identity element in a ring.

Unital ring axiom

The unital ring axiom asserts that a ring $R$ has an element $1\in R$ such that

1\cdot a=a\cdot 1=a\qquad\text{for all }a\in R.

A unital ring is a ring satisfying this axiom. The presence of $1$ allows one to define units (and hence the group of units ) and is typically assumed when discussing standard constructions such as polynomial rings and quotients.