Abstract Let R be a commutative Noetherian ring and I be an ideal of R. Let M be an arbitrary R-module. In this paper we establish some results concerning the cofiniteness properties of modules. It is shown that, M is I-cominimax if and only if there is an ideal with such that M is -cofinite and the R-module is finitely generated, for each Moreover, it is shown that M is I-weakly cofinite if and only if there is an ideal such that V(J) is a finite set and M is -cofinite.

中文翻译：

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共极极大和弱余有限模块的表征

摘要 令 R 为可交换 Noetherian 环，I 为 R 的理想。令 M 为任意 R 模。在本文中，我们建立了一些关于模的余有限性的结果。证明了，M 是 I-cominimax 当且仅当存在一个理想，其中 M 是-余有限且 R-模是有限生成的，而且，对于每个，证明 M 是 I-弱余有限，如果和仅当存在一个理想使得 V(J) 是有限集且 M 是 -cofinite。