Publicação
A note on clean elements and inverses along an element
| Resumo: | Let R be an associative ring with unity 1 and let a, d is an element of R. An element a is an element of R is called invertible along d if there exists unique a(parallel to d) such that a(parallel to d) ad = d = daa(parallel to d) and a(parallel to d )is an element of dR boolean AND Rd (see [6, Definition 4]). In this note, we present new characterizations for the existence of a(parallel to d )by clean decompositions of ad and da. As applications, existence criteria for the Drazin inverse and the group inverse are given. |
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| Autores principais: | Zhu, Huihui |
| Outros Autores: | Patrício, Pedro |
| Assunto: | inverses along an element one-sided inverses along an element clean elements strongly clean decompositions special clean decompositions |
| Ano: | 2018 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | Let R be an associative ring with unity 1 and let a, d is an element of R. An element a is an element of R is called invertible along d if there exists unique a(parallel to d) such that a(parallel to d) ad = d = daa(parallel to d) and a(parallel to d )is an element of dR boolean AND Rd (see [6, Definition 4]). In this note, we present new characterizations for the existence of a(parallel to d )by clean decompositions of ad and da. As applications, existence criteria for the Drazin inverse and the group inverse are given. |
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