# Quotients of PBW-Algebras

In analogy to the affine algebras section in the commutative algebra chapter, we describe OSCAR functionality for dealing with quotients of PBW-algebras modulo two-sided ideals.

Note

Quotients of PBW-algebras modulo two-sided ideals are also known as GR-algebras (here, GR stands for Gröbner-Ready; see Viktor Levandovskyy (2005)).

Example. $\;$ The $n$-th exterior algebra over $K$ is the quotient of the PBW-algebra

$$$A=K \langle e_1,\dots, e_n \mid e_ie_j = - e_je_i \ \text { for }\ i\neq j\rangle$$$

modulo the ideal

$$$\langle e_1^2,\dots, e_n^2\rangle.$$$