Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-08T08:36:48.559Z Has data issue: false hasContentIssue false
  • English
  • Français

Modules with Unique Closure Relative to a Torsion Theory

Published online by Cambridge University Press:  20 November 2018

S. Doğruöz ,
A. Harmanci  and
P. F. Smith
S. Doğruöz
Affiliation:
Adnan Menderes University, Department of Mathematics, Science and Art Faculty, Aydin, Türkiye e-mail: [email protected]
A. Harmanci
Affiliation:
Hacettepe University, Department of Mathematics, Ankara, Türkiye e-mail: [email protected]
P. F. Smith
Affiliation:
University of Glasgow, Department of Mathematics, Glasgow G12 8QW Scotland, UK e-mail: [email protected]
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.

We consider when a single submodule and also when every submodule of a module $M$ over a general ring $R$ has a unique closure with respect to a hereditary torsion theory on Mod-$R$.

Keywords

16S90closed submoduleUC-moduletorsion theory
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 2 , 01 June 2010 , pp. 230 - 238
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Doğruöz, S., Classes of extending modules associated with a torsion theory. East-West J. Math. 8(2006), no. 2, 163–180.Google Scholar
[2] Dung, N. V., Huynh, D. V., Smith, P. F., and Wisbauer, R., Extending Modules. Pitman Research Notes in Mathematics Series 313. Longman, Harlow, 1994.Google Scholar
[3] Smith, P. F., Modules for which every submodule has a unique closure. In: Ring Theory. World Scientific, River Edge, NJ, 1993, pp. 302–313.Google Scholar
[4] Stenström, B., Rings of Quotients. Springer-Verlag, New York, 1975.Google Scholar
[5] Zelmanowitz, J. M., A class of modules with semisimple behavior. In: Abelian Groups and Modules. Math. Appl. 343. Kluwer Academic Publishers, Dordrecht, 1995, pp. 491–500.Google Scholar