Relative Regular Modules. Applications to von Neumann Regular Rings

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• 作者：Leonard D膬u艧 (1) daus@utcb.ro
• 关键词：Regular module – ; Excellent extension – ; Morita equivalent
• 刊名：Applied Categorical Structures
• 出版时间：December 2011
• 出版年：2011
• 期刊代码：8_09272852
• 类别：bio
• 卷：19
• 期：6
• 页码：859-863
• 数据来源：sp

摘要

We use the concept of a regular object with respect to another object in an arbitrary category, in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R −mod and S −mod, when S is an excellent extension of the ring R. Consequently, if S is an excellent extension of the ring R, then S is von Neumann regular ring if and only if R is also von Neumann regular ring. In the second part, using relative regular modules, we give a new proof of a classical result: the von Neumann regular property of a ring is Morita invariant.