Relative regular modules. Applications to von Neumann regular rings

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dc.creatorDaus, Leonard
dc.date2008-03-09
dc.date.accessioned2026-07-07T09:25:53Z
dc.date.available2026-07-07T09:25:53Z
dc.descriptionWe 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.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/0803.1285
dc.identifierhttp://arxiv.org/abs/0803.1285
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156560
dc.subjectRings and Algebras
dc.subject16S20; 16E50; 16D90
dc.titleRelative regular modules. Applications to von Neumann regular rings
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