Relative Regular Modules. Applications to von Neumann Regular Rings |
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Authors: | Leonard Dăuş |
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Affiliation: | 1.Department of Mathematics,Technical University of Civil Engineering,Bucharest 2,Romania |
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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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