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Dergiler / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 3

UC modules with respect to a torsion theory

Mustafa ALKAN
Seçil ÇEKEN
Sayfa
376–385
Yayın Tarihi
2022-11-04
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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].
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Temel Bulgular & Veri:We compare UC and t-UC modules and examine the relationships between them.
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Sonuç & Katkı:We also give some examples of t-UC and UC modules and submodules which have a unique t-closure and unique closure.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hereditary torsion theory · t-closed submodule · UC module

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.

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.

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Bu Makaleye Atıf Yap

ALKAN, M., ÇEKEN, S. (2022). UC modules with respect to a torsion theory. Turkish Journal of Mathematics, Cilt: 36 - Sayı: 3, 376–385. https://ajindex.com/articles/608396

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