Essential extensions and intersection theorems

Author:
W. Schelter

Journal:
Proc. Amer. Math. Soc. **53** (1975), 328-330

MSC:
Primary 16A46

MathSciNet review:
0389971

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Abstract: If is right and left noetherian, primitive factor rings are artinian, and 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 for such a ring.

**[1]**S. A. Amitsur,*Prime rings having polynomial identities with arbitrary coefficients*, Proc. London Math. Soc. (3)**17**(1967), 470–486. MR**0217118****[2]**Robert Gordon and J. C. Robson,*Krull dimension*, American Mathematical Society, Providence, R.I., 1973. Memoirs of the American Mathematical Society, No. 133. MR**0352177****[3]**Arun Vinayak Jategaonkar,*Jacobson’s conjecture and modules over fully bounded Noetherian rings*, J. Algebra**30**(1974), 103–121. MR**0352170****[4]**T. H. Lenagan,*Artinian ideals in Noetherian rings*, Proc. Amer. Math. Soc.**51**(1975), 499–500. MR**0384862**, 10.1090/S0002-9939-1975-0384862-8**[5]**W. Schelter,*Intersection theorems for some non-commutative noetherian rings*(to appear).

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0389971-5

Article copyright:
© Copyright 1975
American Mathematical Society