TY - JOUR

T1 - Embeddings of differential operator rings and goldie dimension

AU - Quinn, Declan

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1988/1

Y1 - 1988/1

N2 - The differential operator ring S = R[x; δ] can be embedded in Ai(R), the first Weyl algebra over R, where R is a Q-algebra and δ is a locally nilpotent derivation on R. Furthermore Ai(R) is again a differential operator ring over the image of S. We consider similar embeddings of the smash product R#U(L), where L is a finite dimensional Lie algebra and U(L) is its universal enveloping algebra. We show that the Weyl algebra over R has the same Goldie dimension as R itself and use this to prove that R and R[x; δ] have the same Goldie dimension where R is again a Q-algebra and δ is locally nilpotent.

AB - The differential operator ring S = R[x; δ] can be embedded in Ai(R), the first Weyl algebra over R, where R is a Q-algebra and δ is a locally nilpotent derivation on R. Furthermore Ai(R) is again a differential operator ring over the image of S. We consider similar embeddings of the smash product R#U(L), where L is a finite dimensional Lie algebra and U(L) is its universal enveloping algebra. We show that the Weyl algebra over R has the same Goldie dimension as R itself and use this to prove that R and R[x; δ] have the same Goldie dimension where R is again a Q-algebra and δ is locally nilpotent.

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U2 - 10.1090/s0002-9939-1988-0915706-x

DO - 10.1090/s0002-9939-1988-0915706-x

M3 - Article

AN - SCOPUS:84966213971

VL - 102

SP - 9

EP - 16

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -