Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The middle annihilator conjecture for embeddable rings


Author: C. Dean
Journal: Proc. Amer. Math. Soc. 103 (1988), 46-48
MSC: Primary 16A34
DOI: https://doi.org/10.1090/S0002-9939-1988-0938642-1
MathSciNet review: 938642
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that any ring which can be embedded in an Artinian ring has just finitely many middle annihilator primes. In particular, this proves the middle annihilator conjecture for a large class of Noetherian rings.


References [Enhancements On Off] (What's this?)

  • [1] W. D. Blair and L. W. Small, Embeddings in Artinian rings and Sylvester rank functions, Israel J. Math. 58 (1987), 10-18. MR 889970 (88i:16016)
  • [2] A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Research Notes in Math., vol. 44, Pitman, London, 1980. MR 590045 (82k:16020)
  • [3] C. Dean and J. T. Stafford, A nonembeddable Noetherian ring, J. Algebra (in press).
  • [4] A. W. Goldie and G. Krause, Strongly regular elements of Noetherian rings, J. Algebra 91 (1984), 410-429. MR 769583 (86d:16003)
  • [5] K. R. Goodearl and R. B. Warfield, Jr., in preparation.
  • [6] R. Gordon, Primary decomposition in right Noetherian rings, Comm. Algebra 2 (1974), 491-524. MR 0360691 (50:13138)
  • [7] A. V. Jategaonkar, Solvable Lie algebras, polycyclic-by-finite groups and bimodule Krull dimension, Comm. Algebra 10 (1982), 19-70. MR 674687 (84i:16014)
  • [8] G. Krause, Middle annihilators in Noetherian rings, Comm. Algebra 8 (1980), 781-791. MR 566421 (81h:16025)
  • [9] A. H. Schofield, Representations of rings over skew fields, London Math. Soc. Lecture Note Ser., vol. 92, Cambridge Univ. Press, London and New York, 1985. MR 800853 (87c:16001)
  • [10] L. W. Small, Rings satisfying a polynomial identity, Lecture notes, Essen, 1980. MR 601386 (82j:16028)
  • [11] L. W. Small and J. T. Stafford, Regularity of zero divisors, Proc. London Math. Soc. (3) 44 (1982), 405-419. MR 656243 (84b:16014)
  • [12] R. B. Warfield, Jr., Prime ideals in ring extensions, J. London Math. Soc. (2) 28 (1983), 453-460. MR 724714 (85e:16006)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A34

Retrieve articles in all journals with MSC: 16A34


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0938642-1
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society