Relative regular modules. Applications to von Neumann regular rings
| Autor: | Daus, Leonard |
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| Rok vydání: | 2008 |
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| Druh dokumentu: | Working Paper |
| Popis: | We use the concept of a regular object with respect to another object in an arbitrary category, defined in \cite{dntd}, 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, we obtain a result of \cite{ps}: 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. Finally, the von Neumann regularity of the Morita ring is investigated. Comment: 6 pages |
| Databáze: | arXiv |
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