Generalizations Of Second Submodules
Küçük Resim Yok
Tarih
2020
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Nis, Fac Sci Math
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this paper, we introduce and study some new generalizations of second submodules via a function phi on the set of all submodules of a module. Let R be a ring with non-zero identity, M be an R-module and phi : S(M) -> S(M) be a function where S(M) is the set of all submodules of M. A non-zero submodule N of M is said to be a phi-second submodule if, for any element a of R and a submodule K of M, aN subset of K and a phi(N) not subset of K imply either N subset of K or a is an element of ann(R)(N). Let n >= 2 be an integer and phi(n) : S(M) -> S(M) be the function defined by phi(n)(L) = (L : (M) ann(R)(L)(n-1)) for every L is an element of S(M). Then a phi(n)-second submodule of M is said to be an n-almost second submodule of M. We determine various algebraic properties of these submodules and investigate their relationships with other known submodule classes such as second, prime and semisimple submodules. We study the structure of n-almost second submodules of modules over ZPI-rings and Dedekind domains. We also give some characterizations of modules and submodules by using n-almost second submodules.
Açıklama
Anahtar Kelimeler
Second Submodule, Phi-Second Submodule, N-Almost Second Submodule, Almost Second Submodule, Dual Notion, Prime, Modules
Kaynak
Filomat
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
34
Sayı
12
