Geodesic
On weakly S-primary submodules
Filomat, Tome 37 (2023) no. 8, p. 2503

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DOI

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :R M) ∩ S = ∅ to be weakly S-primary if there exists s ∈ S such that whenever a ∈ R and m ∈ M with 0 , am ∈ N, then either sa ∈ √(N :R M) or sm ∈ N. We present various properties and characterizations of this concept (especially in faithful multiplication modules). Moreover, the behavior of this structure under module homomorphisms, localizations, quotient modules, cartesian product and idealizations is investigated. Finally, we determine some conditions under which two kinds of submodules of the amalgamation module along an ideal are weakly S-primary.
DOI : 10.2298/FIL2308503Y
Classification : 13A15, 16P40, 16D60
Keywords: S–primary ideal, weakly S-primary ideal, S-primary submodule, weakly S-primary submodule 
Ece Yetkin Celikel; Hani A Khashan. On weakly S-primary submodules. Filomat, Tome 37 (2023) no. 8, p. 2503 . doi: 10.2298/FIL2308503Y
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     author = {Ece Yetkin Celikel and Hani A Khashan},
     title = {On weakly {S-primary} submodules},
     journal = {Filomat},
     pages = {2503 },
     year = {2023},
     volume = {37},
     number = {8},
     doi = {10.2298/FIL2308503Y},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2308503Y/}
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