Mustafa ALKAN, Seçil ÇEKEN

7796

UC modules with respect to a torsion theory

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.

Anahtar Kelimeler:

Hereditary torsion theory, t-closed submodule, UC module, t-UC module

UC modules with respect to a torsion theory

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.

Keywords:

Hereditary torsion theory, t-closed submodule, UC module, t-UC module,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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UC modules with respect to a torsion theory

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