Abstract

Let R be a ring and n, k two non-negative integers. In this paper, we introduce the concepts of n-weak injective and n-weak flat modules and via the notion of special super finitely presented modules, we obtain some characterizations of these modules. We also investigate two classes of modules with richer contents, namely $\mathcal{W}{\mathcal{I}}_k^n(R)$ and $\mathcal{W}{\mathcal{F}}_k^n(R^{op})$ which are larger than that of modules with weak injective and weak flat dimensions at most k. Then over any arbitrary ring, we study the existence of $\mathcal{W}{\mathcal{I}}_k^n(R)$ and $\mathcal{W}{\mathcal{F}}_k^n(R^{op})$ covers and pre-envelopes.

中文翻译：

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n-weak 单射和 n-weak flat 模块的类别相对于特殊的超级呈现模块

摘要

设R是一个环，n , k 是两个非负整数。在本文中，我们介绍了n -weak 单射模块和n -weak flat 模块的概念，并通过特殊的超有限呈现模块的概念，我们获得了这些模块的一些特征。我们还研究了两类内容更丰富的模块，即$\mathcal{宽}{\mathcal{一世}}_{克}^n(\mathrm{电阻})$ 和 $\mathcal{宽}{\mathcal{F}}_{克}^n({\mathrm{电阻}}^{○磷})$它们比具有弱单射和弱平面尺寸的模块更大，最多为k。然后在任意环上，我们研究$\mathcal{宽}{\mathcal{一世}}_{克}^n(\mathrm{电阻})$ 和 $\mathcal{宽}{\mathcal{F}}_{克}^n({\mathrm{电阻}}^{○磷})$ 封面和信封。