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SYMMETRIC GENERALIZED REVERSE $(\alpha, 1)$ BIDERIVATIONS IN RINGS
Keywords:
semiprime ring, prime ring, generalized reverse $(\alpha, 1)$-derivation, generalized reverse $(\alpha, 1)$-biderivation and symmetric generalized reverse $(\alpha, 1)$-biderivationDOI:
https://doi.org/10.17654/0972555522033Abstract
Let $R$ be a ring and $\alpha$ be an endomorphism of $R$. Then, we introduce the notions of generalized reverse $(\alpha, 1)$-derivation and that of symmetric generalized reverse $(\alpha, 1)$-biderivation. It is shown that if a semiprime ring admits a generalized reverse $(\alpha, 1)$-derivation with an associated reverse $(\alpha, 1)$-derivation $d$, then $d$ maps $R$ into $Z(R)$ and also that if a non-commutative prime ring admits a generalized reverse $(\alpha, 1)$-derivation $F$ with an associated reverse $(\alpha, 1)$-derivation $d$, then $F$ is reverse left $\alpha$-multiplier on $R$. Analogous results have been proved for a symmetric generalized reverse $(\alpha, 1)$-biderivation.
Received: July 22, 2022
Revised: October 4, 2022
Accepted: October 13, 2022
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