On gradedJgr-classical 2-absorbing submodules of graded modules over graded commutative rings
| Autor: | Khaldoun Al-Zoubi, Shatha Alghueiri |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
graded 2-absorbing submodule
13a02 graded jgr -classical 2-absorbing submodule 010201 computation theory & mathematics General Mathematics 010102 general mathematics QA1-939 0102 computer and information sciences 0101 mathematics 01 natural sciences 16w50 Mathematics graded classical 2-absorbing submodule |
| Zdroj: | Demonstratio Mathematica, Vol 54, Iss 1, Pp 162-167 (2021) |
| ISSN: | 2391-4661 |
| DOI: | 10.1515/dema-2021-0015 |
| Popis: | LetGbe an abelian group with identityee. LetRbe aG-graded commutative ring with identity 1, andMMbe a gradedR-module. In this paper, we introduce the concept of gradedJgr{J}_{gr}-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some results concerning of these classes of graded submodules. A proper graded submoduleCCofMMis called a gradedJgr{J}_{gr}-classical 2-absorbing submodule ofMM, if wheneverrg,sh,ti∈h(R){r}_{g},{s}_{h},{t}_{i}\in h\left(R)andxj∈h(M){x}_{j}\in h\left(M)withrgshtixj∈C{r}_{g}{s}_{h}{t}_{i}{x}_{j}\in C, then eitherrgshxj∈C+Jgr(M){r}_{g}{s}_{h}{x}_{j}\in C+{J}_{gr}\left(M)orrgtixj∈C+Jgr(M){r}_{g}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M)orshtixj∈C+Jgr(M),{s}_{h}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M),whereJgr(M){J}_{gr}\left(M)is the graded Jacobson radical. |
| Databáze: | OpenAIRE |
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