Journals / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 3
UC modules with respect to a torsion theory
- Pages
- 376–385
- DOI
- —
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 t-closed submodule which was studied in [2]. We compare UC and t-UC modules and examine the relationships between them. We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.
Özet
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 t-closed submodule which was studied in [2]. We compare UC and t-UC modules and examine the relationships between them. We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.