Embedding differential and skew polynomial rings into Artinian rings

Blair, William D.; Small, Lance W.

doi:10.1090/S0002-9939-1990-1025276-5

Embedding differential and skew polynomial rings into Artinian rings
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by William D. Blair and Lance W. Small PDF

Proc. Amer. Math. Soc. 109 (1990), 881-886 Request permission

Abstract:

Under suitable hypotheses it is shown that a differential or skew polynomial ring can be embedded in an Artinian ring provided that its coefficient ring can be embedded in an Artinian ring.

References

William D. Blair and Lance W. Small, Embeddings in Artinian rings and Sylvester rank functions, Israel J. Math. 58 (1987), no. 1, 10–18. MR 889970, DOI 10.1007/BF02764668
Arun Vinayak Jategaonkar, Skew polynomial rings over orders in Artinian rings, J. Algebra 21 (1972), 51–59. MR 299624, DOI 10.1016/0021-8693(72)90033-6
Declan Quinn, Embeddings of differential operator rings and Goldie dimension, Proc. Amer. Math. Soc. 102 (1988), no. 1, 9–16. MR 915706, DOI 10.1090/S0002-9939-1988-0915706-X
Richard Resco, Lance W. Small, and J. T. Stafford, Krull and global dimensions of semiprime Noetherian PI-rings, Trans. Amer. Math. Soc. 274 (1982), no. 1, 285–295. MR 670932, DOI 10.1090/S0002-9947-1982-0670932-1
Lance W. Small, Orders in Artinian rings, J. Algebra 4 (1966), 13–41. MR 200300, DOI 10.1016/0021-8693(66)90047-0
Lance W. Small, Orders in Artinian rings. II, J. Algebra 9 (1968), 266–273. MR 230755, DOI 10.1016/0021-8693(68)90025-2