TY  - JOUR
T1  - On -Quasi-Semiprime Submodules
AU  - Al-zoubi, Khaldoun
AU  - Alghueırı, Shatha
PY  - 2023
DA  - September
DO  - 10.55549/epstem.1351023
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 359
EP  - 363
VL  - 22
LA  - en
AB  - Let G be a group. A ring R is called a graded ring (or G-graded ring) if there exist additive subgroups Rα of R indexed by the elements α∈G such that R=⊕α∈GRαand RαRβ⊆Rαβ for all α, β∈G. If an element of R belongs to h(R)=∪α∈GRα, then it is called homogeneous. A Left R-module M is said to be a graded R-module if there exists a family of additive subgroups {Mα} α∈G of M such that M=⊕α∈GMα and RαMβ⊆Mαβ or all α,β∈G. Also if an element of M belongs to ∪α∈GMα=h(M), then it is called homogeneous. A submodule N of M is said to be a graded submodule of M if N=⊕α∈GN∩Mα:=⊕α∈GNα. Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. A proper graded submodule S of M is said to be a gr-semiprime submodule if whenever rⁿm∈S where r∈h(R), m∈h(M) and n∈Z⁺, then rm∈S. In this work, we introduce the concept of gr-quasi-semiprime submodule as a generalization of gr-semiprime submodule and give some basic properties of these classes of graded submodules. We say that a proper graded submodule S of M is a gr-quasi-semiprime submodule if (S:RM) is a gr-semiprime ideal of R.
KW  - Graded quasi-semiprime submodule
KW  - Graded semiprime submodule
KW  - Graded prime
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UR  - https://doi.org/10.55549/epstem.1351023
L1  - https://dergipark.org.tr/en/download/article-file/3366949
ER  -