r-Submodules and sr-Submodules
TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.4, ss.1863-1876, 2018 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 42 Sayı: 4
- Basım Tarihi: 2018
- Doi Numarası: 10.3906/mat-1702-20
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1863-1876
- Anahtar Kelimeler: r-Ideal, prime ideal, r-submodule, special r-submodule, prime submodule, PRIME SUBMODULES
- Marmara Üniversitesi Adresli: Evet
Özet
In this article, we introduce new classes of submodules called r-submodule and special r-submodule, which are two different generalizations of r-ideals. Let M be an R-module, where R is a commutative ring. We call a proper submodule N of M an r-submodule (resp., special r-submodule) if the condition am is an element of N with ann(M) (a) = 0(M) (resp., ann(R)(m) = 0) implies that m E N (resp., a is an element of (N :(R) M)) for each a is an element of R and m is an element of M. We also give various results and examples concerning r-submodules and special r-submodules.