Geodesic
Characterizations and representations of w-core inverses in rings
Filomat, Tome 37 (2023) no. 10, p. 3183

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DOI

Let R be an associate ring with involution and let a, w ∈ R. The notion of EI along an element is introduced. An element w is called EI along a if w ∥a exists and w ∥a w = ww ∥a. Its several characterizations are given by w-core inverses. Several necessary and sufficient conditions such that a # w aw and wa # w a are projections are derived. In particular, it is shown that a # w aw is a projection if and only if aw is Moore-Penrose invertible with (aw) † = a # w if and only if aw is group invertible with (aw) # = a # w. Also, wa # w a is a projection if and only if a is Moore-Penrose invertible with a † = wa # w. Then, we describe the existence of w-core inverse of a by the existence of (the unique) projection p ∈ R and idempotent q ∈ R satisfying pR = aR = awR = qR and Rq = Raw.
DOI : 10.2298/FIL2310183Z
Classification : 15A09, 16W10
Keywords: The w-core inverses, the inverse along an element, {1, 3}-inverses, {1, 4}-inverses, Moore-Penrose inverses 
Qi Zhang; Chengcheng Wang; Huihui Zhu. Characterizations and representations of w-core inverses in rings. Filomat, Tome 37 (2023) no. 10, p. 3183 . doi: 10.2298/FIL2310183Z
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     title = {Characterizations and representations of w-core inverses in rings},
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     year = {2023},
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     doi = {10.2298/FIL2310183Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2310183Z/}
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