Revista de la
Unión Matemática Argentina
One-sided EP elements in rings with involution
Cang Wu, Jianlong Chen, and Yu Chen

Volume 67, no. 2 (2024), pp. 517–528    

Published online (final version): October 7, 2024

https://doi.org/10.33044/revuma.3572

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Abstract

This paper investigates the one-sided EP property of elements in rings with involution. Let $R$ be a ring with involution $\ast$. Then $a \in R$ is said to be left (resp. right) EP if $a$ is Moore–Penrose invertible and $aR \subseteq a^{\ast}R$ (resp. $a^{\ast}R \subseteq aR$). Many properties of EP elements are extended to one-sided versions. Some new characterizations of EP elements are presented in relation to the absorption law for Moore–Penrose inverses.

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