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    Article

    Left and Right Weighted (b, c)-inverse in Rings and Its Applications

    In this paper, left and right (v, w)-weighted (b, c)-inverse in rings are introduced. Let R be a ring and a, b, c, v, w ∈ R. The element x ∈ R is called a left (v, w)-weighted (b, c)-inverse of a if Rx ∈ Rc and x...

    Sanzhang Xu in Frontiers of Mathematics (2024)

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    Article

    New characterizations for the weighted (b, c)-inverse in rings and their applications

    In this paper, necessary and sufficient conditions for a to be (v, w)-weighted (b, c)-invertible are given, where a, b, c, v, w are elements of a unital ring. The relationships between the (v, w)-weighted (b, c)-...

    Sanzhang Xu, Dingguo Wang, Julio Benítez in Revista de la Real Academia de Ciencias Ex… (2023)

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    Article

    Core invertibility of triangular matrices over a ring

    We obtained several equivalent conditions for the existence of core inverses and dual core inverses of triangular matrices over a ring with involution. As applications, some necessary and sufficient conditions...

    Sanzhang Xu in Indian Journal of Pure and Applied Mathematics (2019)

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    Article

    EP Elements in Rings with Involution

    Let R be a unital ring with involution. We first show that the EP elements in R can be characterized by three equations. Namely, let $...

    Sanzhang Xu, Jianlong Chen, Julio Benítez in Bulletin of the Malaysian Mathematical Sci… (2019)

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    Article

    Centralizer’s applications to the (b, c)-inverses in rings

    We give several conditions in order that the absorption law for one sided (b, c)-inverses in rings holds. Also, by using centralizers, we obtain the absorption law for the (b, c)-inverse and the reverse order law...

    Sanzhang Xu, Jianlong Chen, Julio Benítez… in Revista de la Real Academia de Ciencias Ex… (2019)

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    Article

    On Characterizations of Special Elements in Rings with Involution

    Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element, the authors answer in this paper. Several ...

    Sanzhang Xu, Jianlong Chen, Dijana Mosić in Chinese Annals of Mathematics, Series B (2019)

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    Article

    Existence Criteria and Expressions of the (b, c)-Inverse in Rings and Their Applications

    Let R be a ring. Existence criteria for the (b, c)-inverse are given. We present explicit expressions for the (b, c)-inverse by using inner inverses. We answer the question when the (b, c)-inverse of ...

    Sanzhang Xu, Julio Benítez in Mediterranean Journal of Mathematics (2018)

  8. No Access

    Article

    New characterizations for core inverses in rings with involution

    The core inverse for a complex matrix was introduced by O. M. Baksalary and G. Trenkler. D. S. Rakić, N. Č. Dinčić and D. S. Djordjević generalized the core inverse of a complex matrix to the case of an elemen...

    Sanzhang Xu, Jianlong Chen, **aoxiang Zhang in Frontiers of Mathematics in China (2017)