Abstract
This article establishes a few sufficient conditions of the forward-order law for the core inverse of elements in rings with involution. It also presents the forward-order law for the weighted core inverse and the triple forward-order law for the core inverse. Additionally, we discuss the hybrid forward-order law involving different generalized inverses like the Moore–Penrose inverse, the group inverse, and the core inverse.
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Acknowledgements
The authors thank the anonymous referee for carefully reading the earlier draft and for suggestions that improved the article’s presentation. The first author acknowledges the support of the Council of Scientific and Industrial Research-University Grants Commission, India. We thank Aaisha Be and Vaibhav Shekhar for their helpful suggestions on some parts of this article.
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Kumar, A., Mishra, D. On forward-order law for core inverse in rings. Aequat. Math. 97, 537–562 (2023). https://doi.org/10.1007/s00010-022-00933-y
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DOI: https://doi.org/10.1007/s00010-022-00933-y