Atıf İçin Kopyala
Aslankarayiğit Uğurlu E., Koç S., Tekir Ü.
COMMUNICATIONS IN ALGEBRA, cilt.51, sa.5, ss.1-10, 2023 (SCI-Expanded)
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Yayın Türü:
Makale / Tam Makale
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Cilt numarası:
51
Sayı:
5
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Basım Tarihi:
2023
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Doi Numarası:
10.1080/00927872.2022.2164772
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Dergi Adı:
COMMUNICATIONS IN ALGEBRA
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Derginin Tarandığı İndeksler:
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
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Sayfa Sayıları:
ss.1-10
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Marmara Üniversitesi Adresli:
Evet
Özet
In this paper, we study S-Principal ideal multiplication modules. Let A " role="presentation" >A be a commutative ring with 1≠0, S⊆A" role="presentation" >1≠0, S⊆A a multiplicatively closed set and M " role="presentation" >M an A-module. A submodule N of M is said to be an S-multiple of M if there exist s∈S" role="presentation" >s∈S and a principal ideal I of A such that sN⊆IM⊆N" role="presentation" >sN⊆IM⊆N. M " role="presentation" >M is said to be an S-principal ideal multiplication module if every submodule N " role="presentation" >N of M " role="presentation" >M is an S-multiple of M. Various examples and properties of S-principal ideal multiplication modules are given. We investigate the conditions under which the trivial extension A⋉M" role="presentation" >A⋉M is an S⋉0" role="presentation" >S⋉0-principal ideal ring. Also, we prove Cohen type theorem for S-principal ideal multiplication modules in terms of S-prime submodules.