Please use this identifier to cite or link to this item: http://hdl.handle.net/1822/2888

 Title: Generalized invertibility in two semigroups of a ring Author(s): Patrício, PedroPuystjens, Roland Keywords: Generalized invertibilityCorner ringsMatrices over ringsSemigroups Issue date: 15-Jan-2004 Publisher: Elsevier Journal: Linear Algebra and its Applications Citation: "Linear Algebra and its Applications". ISSN 0024-3795. 377 (2004) 125-139. Abstract(s): In {\em Linear and Multilinear Algebra}, 1997, Vol.43, pp.137-150, R. Puystjens and R. E. Hartwig proved that given a regular element $t$ of a ring $R$ with unity $1$, then $t$ has a group inverse if and only if $u=t^{2}t^{-}+1-tt^{-}$ is invertible in $R$ if and only if $v=t^{-}t^{2}+1-t^{-}t$ is invertible in $R$. There, R. E. Hartwig posed the pertinent question whether the inverse of $u$ and $v$ could be directly related. Similar equivalences appear in the characterization of Moore-Penrose and Drazin invertibility, and therefore analogous questions arise. We present a unifying result to answer these questions not only involving classical invertibility, but also some generalized inverses as well. Type: Article URI: http://hdl.handle.net/1822/2888 DOI: 10.1016/j.laa.2003.08.004 ISSN: 0024-3795 Publisher version: http://www.elsevier.com/wps/find/journaldescription.cws_home/522483/description#description Peer-Reviewed: yes Access: Open access Appears in Collections: CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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