Abstract The minus partial order is already known for sets of matrices over a field and bounded linear operators on arbitrary Hilbert spaces. Recently, this partial order has been studied on Rickart rings. In this paper, we extend the concept of the minus relation to the module theoretic setting and prove that this relation is a partial order when the module is regular. Moreover, various characterizations of the minus partial order in regular modules are presented and some well-known results are also generalized.

中文翻译：

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常规模块中的减偏序

摘要 对于域上的矩阵集和任意希尔伯特空间上的有界线性算子，负偏序是已知的。最近，在 Rickart 环上研究了这种偏序。在本文中，我们将负关系的概念扩展到模理论设置，并证明当模是正则时，这种关系是偏序的。此外，还介绍了正则模块中负偏序的各种特征，并概括了一些众所周知的结果。