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.
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
\[\langle e_1^2,\dots, e_n^2\rangle.\]