Abstract
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 xvawb = b and dually y ∈ R is called a right (v, w)-weighted (b, c)-inverse of a if yR ⊆ bR and cvawy = c. Existence criteria for left and right (v, w)-weighted (b, c)-inverse of a are given. We also present explicit expressions for left and right weighted (b, c)-inverse by using inner inverses. As applications, several equivalent conditions for an element in a ring to be (v, w)-weighted (b, c)-invertible are obtained. Moreover, commuting properties of the (v, w)-weighted (b, c)-inverse are investigated.
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Acknowledgements
The research article is supported by the National Natural Science Foundation of China (No. 12001223), the Qing Lan Project of Jiangsu Provincethe, the Natural Science Foundation of Jiangsu Province of China (No. BK20220702) and “Five-Three-Three” talents of Huai’an city.
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Xu, S. Left and Right Weighted (b, c)-inverse in Rings and Its Applications. Front. Math (2024). https://doi.org/10.1007/s11464-020-0088-x
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DOI: https://doi.org/10.1007/s11464-020-0088-x