Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T21:43:05.704Z Has data issue: false hasContentIssue false
  • English
  • Français

Distributive Modules

Published online by Cambridge University Press:  20 November 2018

V. Erdoğdu
V. Erdoğdu*
Affiliation:
University of Bahrain P.O. Box 1082, Bahrain
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.

Let R be a commutative ring with identity. An R-module M is said to be distributive if the lattice of submodules of M is distributive. We characterize such modules and study their properties.

Keywords

Primary 13C1313C12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 248 - 254
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Atiyah, M.F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley, Reading, Mass. (1969).Google Scholar
2. Cohn, P.M., Algebra, Vol. 2 Wiley (1977).Google Scholar
3. Davison, T. M.K., Distributive homomorphism of rings and modules, J. Reine Angew. Math. 270 (1974), pp. 28–34.Google Scholar
4. Gilmer, R.W., Multiplicative Ideal Theory, Marcel Dekker, New York (1972).Google Scholar
5. Knight, J.T., Commutative Algebra, L.M.S. Lecture Notes (1971).Google Scholar
6. Larsen, M.D. and McCarthy, P.J., Multiplicative Theory of Ideals, Academic Press, New York (1971).Google Scholar
7. Stephenson, W., Modules whose lattice of submodules is distributive, Proc. London Math. Soc. (3)28 (1974), pp. 291–310.Google Scholar
8. Zariski, O. and Samuel, P., Commutative Algebra, Vol. 1, Princeton, Van Nostrand (1958).Google Scholar