On graded \(I_e\)-primary submodules of graded modules over graded commutative rings. (English) Zbl 1499.13001
Summary: Let \(G\) be a group with identity \(e\). Let \(R\) be a \(G\)-graded commutative ring with identity and \(M\) a graded \(R\)-module. In this paper, we introduce the concept of graded \(J_e\)-primary submodule as a generalization of a graded primary submodule for \(J=\bigoplus_{g\in G}J_g\) a fixed graded ideal of \(R\). We give a number of results concerning of these classes of graded submodules and their homogeneous components. A proper graded submodule \(C\) of \(M\) is said to be a graded \(J_e\)-primary submodule of \(M\) if whenever \(r_h\in h(R)\) and \(m_{\lambda}\in h(M)\) with \(r_h m_{\lambda}\in C\backslash J_e C\), implies either \(m_{\lambda}\in C\) or \(r_h\in \mathrm{Gr}((C:_R M))\).
MSC:
| 13A02 | Graded rings |
Keywords:
graded \(I_e\)-primary submodules; graded \(I_e\)-prime submodules; graded primary submodulesReferences:
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