Representations of the (b, c)-Inverses in Rings with Involution

Yuanyuan Ke, Yuefeng Gao, Jianlong Chen


Let R be a ring and b, and c in R. The concept of (b; c)-inverses was introduced by Drazin in 2012. In this paper, necessary and sucient conditions for the existence of the (b; c)-inverse in a ring with an involution are investigated, and new expressions for them are derived. A new representation of the (b; c)-inverse based on the group inverse is also presented.

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