Turkish Journal of Mathematics
Abstract
In this paper, we give some characterizations of modules M over a ring R such that every submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using the concept of \tau-closed submodule which was studied in [2]. We compare UC and \tau-UC modules and examine the relationships between them. We also give some examples of \tau-UC and UC modules and submodules which have a unique \tau-closure and unique closure.
DOI
10.3906/mat-1009-33
Keywords
Hereditary torsion theory, \tau-closed submodule, UC module, \tau-UC module
First Page
376
Last Page
385
Recommended Citation
ÇEKEN, S, & ALKAN, M (2012). UC modules with respect to a torsion theory. Turkish Journal of Mathematics 36 (3): 376-385. https://doi.org/10.3906/mat-1009-33
