Let R a commutative ring with identity and M be a unitary R-module. In this paper, we investigate some properties of n-absorbing submodules of M as a generalization of 2-absorbing submodules. We also define the classical n-absorbing submodule, a proper submodule N of an R-module M is called a classical n-absorbing submodule if whenever \(a_1 a_2\ldots a_{n+1} m\in N\) for \(a_1, a_2,\ldots , a_{n+1}\in R\) and \(m \in M\), there are n of \(a_i\)’s whose product with m is in N. Furthermore, we give some characterizations of n-absorbing and classical n-absorbing submodules under some conditions.

中文翻译：

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在经典的n吸收子模块上

让ř与身份交换环和中号是整体- [R -模。在本文中，我们将M的n个吸收子模块的一些性质作为2个吸收子模块的推广。我们还定义了经典Ñ -absorbing子模块，一个适当的子模块Ñ一个的[R -模中号被称为经典Ñ -absorbing子模块如果每当\（A_1 A_2 \ ldots A_ {N + 1} M \于N \）为\ （A_1，A_2，\ ldots，A_ {N + 1} \中的R \）和\（以M \米\） ，有ñ的\（A_I \）与m的乘积在N中。此外，我们给出了在某些条件下吸收n和经典吸收n子模块的一些特征。