Unital Algebra

In mathematics, a unital algebra or unitary algebra is an algebra which contains a multiplicative identity element (or unit), i.e. an element 1 with the property 1x = x1 = x for all elements x of the algebra.

Most associative algebras considered in abstract algebra, for instance group algebras, polynomial algebras and matrix algebras, are unital, if rings are taken to be so. Most algebras of functions considered in analysis are not unital, for instance the algebra of functions decreasing to zero at infinity, especially those with compact support on some (non-compact) space.