A note on clean elements and inverses along an element
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, Defi...
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| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2018
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| Texto completo: | http://hdl.handle.net/1822/66087 |
| País: | Portugal |
| Oai: | oai:repositorium.sdum.uminho.pt:1822/66087 |
| 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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