Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T13:48:53.221Z Has data issue: false hasContentIssue false
  • English
  • Français

On Modules Having Small Cofinite Irreducibles

Published online by Cambridge University Press:  20 November 2018

E. W. Johnson ,
Johnny A. Johnson  and
Monty B. Taylor
E. W. Johnson
Affiliation:
Department of Mathematics, University of Iowa Iowa City, Iowa 55242 U.S.A.
Johnny A. Johnson
Affiliation:
Department of Mathematics, University of Houston Houston, Texas 77204 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we obtain several new characterizations of modules having small cofinite irreducibles. One of these characterizations involves a metric topology defined on the submodule lattice.

Keywords

13C0513E05moduleslocal ringssubmodules
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 490 - 494
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Anderson, D. D., The existence of dual modules, Proc. Amer. Math. Soc. 55(1976), 258–260.Google Scholar
2. Hochster, M., Cyclic purity versus purity in excellent Noetherian rings, Trans. Amer. Math. Soc. 231(1977), 463–487.Google Scholar
3. Johnson, E. W., Modules: duals and principally fake duals, Algebra Universalis 24(1987), 111–119.Google Scholar
4. Johnson, E. W. and Johnson, J. A., Lattice modules over semi-local Noether lattices, Fund. Math. 68(1970), 187–201.Google Scholar
5. Johnson, J. A. and Taylor, M. B., New characterizations of approximately Gorenstein rings, Glasgow Math. J. 34(1992), 361–363. 6.1. Kaplansky, Commutative rings, Allyn and Bacon, Boston, 1970.Google Scholar
7. Larsen, M. D. and McCarthy, P. J., Multiplicative Theorey of Ideals, Academic Press, New York and London, 1971.Google Scholar
8. Lu, Chin-Pi, Quasi-complete modules, Indiana Univ. Math. J. 29(1980), 277–286.Google Scholar
9. Nagata, M., Local rings, Interscience Tracts in Pure and Appl. Math. 13, Interscience, New York, 1962.Google Scholar
10. Northcott, D. G., Lessons on Rings, Modules and Multiplicities, Cambridge Univ. Press, London and New York, 1968.Google Scholar
11. Northcott, D. G. and Rees, D., Principal systems, Quart. J. Math. Oxford Ser. (2) 8(1957), 119–127.Google Scholar
12. Zariski, O. and Samuel, P., Commutative Algebra, Vol. II, Springer-Verlag, New York, 1960.Google Scholar