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)



Non-Artinian essential extensions of simple modules

Authors: K. R. Goodearl and A. H. Schofield
Journal: Proc. Amer. Math. Soc. 97 (1986), 233-236
MSC: Primary 16A33
MathSciNet review: 835871
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A noetherian ring of Krull dimension one is constructed which possesses a simple module with a cyclic non-artinian essential extension. The construction also provides an example of a torsionfree noetherian bimodule which fails to satisfy Jategaonkar's density condition.

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

  • [1] A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Pitman, London, 1980. MR 590045 (82k:16020)
  • [2] R. Gordon and J. C. Robson, Krull dimension, Mem. Amer. Math. Soc. no. 133 (1973). MR 0352177 (50:4664)
  • [3] A. V. Jategaonkar, Jacobson's conjecture and modules over fully bounded noetherian rings, J. Algebra 30 (1974), 103-121. MR 0352170 (50:4657)
  • [4] -, Solvable Lie algebras, polycyclic-by-finite groups, and bimodule Krull dimension, Comm. Algebra 10 (1982), 19-69. MR 674687 (84i:16014)
  • [5] T. H. Lenagan, Noetherian rings with Krull dimension one, J. London Math. Soc. (2) 15 (1977), 41-47. MR 0442008 (56:397)
  • [6] I. M. Musson, Injective modules for group rings of polycyclic groups. II, Quart. J. Math. Oxford Ser. (2) 31 (1980), 449-466. MR 596979 (82g:16019)
  • [7] -, Some examples of modules over noetherian rings, Glasgow Math. J. 23 (1982), 9-13. MR 641613 (83g:16029)
  • [8] A. H. Schofield, Artin's problem for skew field extensions, Math. Proc. Cambridge Philos. Soc. 97 (1985), 1-6. MR 764488 (86e:16029)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A33

Retrieve articles in all journals with MSC: 16A33

Additional Information

Keywords: Noetherian ring, simple module, essential extension
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society