Geodesic
The Moore-Penrose inverse in rings with involution
Filomat, Tome 33 (2019) no. 18, p. 5791

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DOI

Let R be a unital ring with involution. In this paper, we first show that for an element a ∈ R, a is Moore-Penrose invertible if and only if a is well-supported if and only if a is co-supported. Moreover, several new necessary and sufficient conditions for the existence of the Moore-Penrose inverse of an element in a ring R are obtained. In addition, the formulae of the Moore-Penrose inverse of an element in a ring are presented
DOI : 10.2298/FIL1918791X
Classification : 15A09, 16W10, 16U80
Keywords: Moore-Penrose inverse, Group inverse, EP element, Normal element, Hermitian element, Projection 
Sanzhang Xu; Jianlong Chen. The Moore-Penrose inverse in rings with involution. Filomat, Tome 33 (2019) no. 18, p. 5791 . doi: 10.2298/FIL1918791X
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     author = {Sanzhang Xu and Jianlong Chen},
     title = {The {Moore-Penrose} inverse in rings with involution},
     journal = {Filomat},
     pages = {5791 },
     year = {2019},
     volume = {33},
     number = {18},
     doi = {10.2298/FIL1918791X},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL1918791X/}
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