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arXiv · 2303.06651

On WD and WDMP generalized inverses in rings

Amit Kumar·Debasisha Mishra
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Abstract

Motivated by the very recent work of Gao, Y., Chen, J., Wang, J., Zou, H. [Comm. Algebra, 49(8) (2021) 3241-3254; MR4283143], we introduce two new generalized inverses named weak Drazin (WD) and weak Drazin Moore-Penrose (WDMP) inverses for elements in rings. A few of their properties are then provided, and the fact that the proposed generalized inverses coincide with different well-known generalized inverses under certain assumptions is established. Further, we discuss additive properties, reverse-order law and forward-order law for WD and WDMP generalized inverses. Some examples are also provided in support of the theoretical results.

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Amit Kumar, Debasisha Mishra. 2023-03-12. On WD and WDMP generalized inverses in rings. https://doi.org/10.2298/fil2416681k

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