On graded 2-absorbing submodules over \(Gr\)-multiplication modules. (English) Zbl 1474.13003
Summary: Let \(G\) be a multiplicative group with identity \(e\), \(R\) be a \(G\)-graded commutative ring and \(M\) be a graded \(R\)-module. The aim of this article is some investigations of graded \(2\)-absorbing submodules over \(Gr\)-multiplication modules. A graded submodule \(N\) of \(R\)-module \(M\) is called graded \(2\)-absorbing if whenever \(a,b\in h(R)\) and \(m\in h(M)\) with \(abm\in N\), then either \(ab\in (N :_R M)\) or \(am\in N\) or \(bm\in N\). We also introduce the concept of graded classical \(2\)-absorbing submodule as a generalization of graded classical prime submodules and show a number of results in this class.
Keywords:
graded multiplication modules; graded prime submodules; graded 2-absorbing submodules; graded classical submodules; graded classical 2-absorbing submodulesReferences:
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