In algebra, an **augmentation** of an associative algebra *A* over a commutative ring *k* is a *k*-algebra homomorphism , typically denoted by ε. An algebra together with an augmentation is called an **augmented algebra**. The kernel of the augmentation is a two-sided ideal called the augmentation ideal of *A*.

For example, if is the group algebra of a finite group *G*, then

is an augmentation.

If *A* is a graded algebra which is connected, i.e. , then the homomorphism which maps an element to its homogeneous component of degree 0 is an augmentation. For example,

is an augmentation on the polynomial ring .