Abstract
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.
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Dăuş, L. Relative Regular Modules. Applications to von Neumann Regular Rings. Appl Categor Struct 19, 859–863 (2011). https://doi.org/10.1007/s10485-009-9203-6
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DOI: https://doi.org/10.1007/s10485-009-9203-6