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In this paper, the generalized inverse of element in an associative ring is studied.Two kinds of new generalized inverses named gao zhou inverse and F-generalized zhou inverse are proposed and their properties will be thoroughly revealed.From the properties, it can be seen that the F-generalized zhou inverse is between the generalized zhou inverse and the Drazin inverse, and the gao zhou inverse is the generalization of zhou inverse.
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Yang et al. (2024) studied this question.
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