Essential extensions and intersection theorems
HTML articles powered by AMS MathViewer
- by W. Schelter PDF
- Proc. Amer. Math. Soc. 53 (1975), 328-330 Request permission
Abstract:
If $R$ is right and left noetherian, primitive factor rings are artinian, and $R$ is right fully bounded, then a simple proof is given to show that finitely generated essential extensions of right artinian modules are artinian. An immediate corollary is that $\cap _{n = 1}^\infty {J^n} = 0$ for such a ring.References
- S. A. Amitsur, Prime rings having polynomial identities with arbitrary coefficients, Proc. London Math. Soc. (3) 17 (1967), 470–486. MR 217118, DOI 10.1112/plms/s3-17.3.470
- Robert Gordon and J. C. Robson, Krull dimension, Memoirs of the American Mathematical Society, No. 133, American Mathematical Society, Providence, R.I., 1973. MR 0352177
- Arun Vinayak Jategaonkar, Jacobson’s conjecture and modules over fully bounded Noetherian rings, J. Algebra 30 (1974), 103–121. MR 352170, DOI 10.1016/0021-8693(74)90195-1
- T. H. Lenagan, Artinian ideals in Noetherian rings, Proc. Amer. Math. Soc. 51 (1975), 499–500. MR 384862, DOI 10.1090/S0002-9939-1975-0384862-8 W. Schelter, Intersection theorems for some non-commutative noetherian rings (to appear).
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 328-330
- MSC: Primary 16A46
- DOI: https://doi.org/10.1090/S0002-9939-1975-0389971-5
- MathSciNet review: 0389971