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Weighted w -core inverses in rings

Liyun Wu, Huihui Zhu (2023)

Czechoslovak Mathematical Journal

Let R be a unital * -ring. For any a , s , t , v , w ∈ R we define the weighted w -core inverse and the weighted dual s -core inverse, extending the w -core inverse and the dual s -core inverse, respectively. An element a ∈ R has a weighted w -core inverse with the weight v if there exists some x ∈ R such that a w x v x = x , x v a w a = a and ( a w x ) * = a w x . Dually, an element a ∈ R has a weighted dual s -core inverse with the weight t if there exists some y ∈ R such that y t y s a = y , a s a t y = a and ( y s a ) * = y s a . Several characterizations of weighted w -core invertible and weighted dual s -core invertible...

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