On S-prime submodules

Esra Şengelen SEVİM; Tarik ARABACI; Ünsal TEKİR; Suat KOÇ

Makale detayları

On S-prime submodules

Yazarlar:

Esra Şengelen SEVİM | Tarik ARABACI | Ünsal TEKİR | Suat KOÇ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.1036-1046

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745667

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

In this study, we introduce the concepts of SSS-prime submodules and\ SSS%  -torsion-free modules, which are generalizations of prime submodules and  torsion-free modules. Suppose S⊆R S⊆R S\subseteq R\ is a multiplicatively closed  subset of a commutative ring R R\ R, and let MMM be a unital RRR-module. A  submodule P P P\ of M M M\ with (P:RM)∩S=∅(P:RM)∩S=∅(P:_{R}M)\cap S=\emptyset is called an SSS%  -prime submodule if there is an s∈Ss∈Ss\in S\ such that am∈Pam∈Pam\in P implies %  sa\in(P:_{R}M)\ or sm∈P. sm∈P. sm\in P.\ Also, an RRR-module M M M\ is called SSS%  -torsion-free if ann(M)∩S=∅ann(M)∩S=∅ann(M)\cap S=\emptyset and there exists s∈S s∈S s\in S\ such  that am=0 am=0 am=0\ implies sa=0 sa=0 sa=0\ or sm=0 sm=0 sm=0\ for each a∈R a∈R a\in R\ and m∈M. m∈M. m\in M.\ In  addition to giving many properties of SSS-prime submodules, we characterize  certain prime submodules in terms of SSS-prime submodules. Furthermore,  using these concepts, we characterize some classical modules such as simple  modules, SSS-Noetherian modules, and torsion-free modules.

Makale detayları

On S-prime submodules

Yazarlar: Esra Şengelen SEVİM | Tarik ARABACI | Ünsal TEKİR | Suat KOÇ

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.1036-1046

Belge Tipi: Makale

Yayın Tarihi: 3/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745667

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Esra Şengelen SEVİM | Tarik ARABACI | Ünsal TEKİR | Suat KOÇ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.1036-1046

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745667

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098