Exact embeddings into Artinian rings
HTML articles powered by AMS MathViewer
- by Raymond A. Beaulieu and Anders Jensen
- Proc. Amer. Math. Soc. 118 (1993), 391-399
- DOI: https://doi.org/10.1090/S0002-9939-1993-1129872-9
- PDF | Request permission
Abstract:
The concept of exact embedding of a Noetherian ring into an Artinian ring discussed by Blair and Small is exploited to yield results on embeddings of various rings into Artinian rings. In particular we investigate Ore extensions, group graded rings, and filtered rings. Also, we prove that exact embeddability is a Morita invariant.References
- Maria Jesus Asensio, Michel Van den Bergh, and Freddy Van Oystaeyen, A new algebraic approach to microlocalization of filtered rings, Trans. Amer. Math. Soc. 316 (1989), no. 2, 537–553. MR 958890, DOI 10.1090/S0002-9947-1989-0958890-X
- A. D. Bell and K. R. Goodearl, Uniform rank over differential operator rings and Poincaré-Birkhoff-Witt extensions, Pacific J. Math. 131 (1988), no. 1, 13–37. MR 917863
- 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
- William D. Blair and Lance W. Small, Embedding differential and skew polynomial rings into Artinian rings, Proc. Amer. Math. Soc. 109 (1990), no. 4, 881–886. MR 1025276, DOI 10.1090/S0002-9939-1990-1025276-5
- M. Cohen and S. Montgomery, Group-graded rings, smash products, and group actions, Trans. Amer. Math. Soc. 282 (1984), no. 1, 237–258. MR 728711, DOI 10.1090/S0002-9947-1984-0728711-4
- C. Dean, Nonembeddable factors of the enveloping algebras of semisimple Lie algebras, Bull. London Math. Soc. 21 (1989), no. 1, 65–69. MR 967792, DOI 10.1112/blms/21.1.65
- C. Dean and J. T. Stafford, A nonembeddable Noetherian ring, J. Algebra 115 (1988), no. 1, 175–181. MR 937608, DOI 10.1016/0021-8693(88)90289-X
- Arun Vinayak Jategaonkar, Relative Krull dimension and prime ideals in right Noetherian rings, Comm. Algebra 2 (1974), 429–468. MR 357494, DOI 10.1080/00927877408822020 A. Jensen and S. Jøndrup, Classical quotient rings of group graded rings (to appear). A. Jensen, S. Jøndrup and M. Van Den Bergh, Artinian quotient rings of filtered rings (to appear).
- Günter Krause, Middle annihilators in Noetherian rings, Comm. Algebra 8 (1980), no. 8, 781–791. MR 566421, DOI 10.1080/00927878008822489
- Günter Krause, Additive rank functions in Noetherian rings, J. Algebra 130 (1990), no. 2, 451–461. MR 1051313, DOI 10.1016/0021-8693(90)90092-3
- J. C. McConnell and J. C. Robson, Noncommutative Noetherian rings, Pure and Applied Mathematics (New York), John Wiley & Sons, Ltd., Chichester, 1987. With the cooperation of L. W. Small; A Wiley-Interscience Publication. MR 934572
- D. S. Passman, Prime ideals in enveloping rings, Trans. Amer. Math. Soc. 302 (1987), no. 2, 535–560. MR 891634, DOI 10.1090/S0002-9947-1987-0891634-7
- A. H. Schofield, Representation of rings over skew fields, London Mathematical Society Lecture Note Series, vol. 92, Cambridge University Press, Cambridge, 1985. MR 800853, DOI 10.1017/CBO9780511661914
- Lance W. Small, Orders in Artinian rings. II, J. Algebra 9 (1968), 266–273. MR 230755, DOI 10.1016/0021-8693(68)90025-2
- Lance W. Small, The embedding problem for Noetherian rings, Bull. Amer. Math. Soc. 75 (1969), 147–148. MR 232797, DOI 10.1090/S0002-9904-1969-12183-X
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 391-399
- MSC: Primary 16P40; Secondary 16S36, 16W50, 16W60
- DOI: https://doi.org/10.1090/S0002-9939-1993-1129872-9
- MathSciNet review: 1129872