Maximality of pbw extensions of orders

摘要

It is shown that if R is a maximal order in a simple Artinian ring Q, then any PBW extension 5 of R is also a maximal order in a simple Artinian ring. Furthermore, if R is Noetherian, the maximal v-ideals of S are either induced from R or cut down from QS, and a representation of 5 using localizations at these maximal v-ideals is given.