The goal of this study is to bring out the following conclusion: Let $\mathcal{R}$ be a non-commutative prime ring of characteristic not two and $\mathcal{D}$ be a bi-semiderivation on $\mathcal{R}$ with a function $\mathfrak{f}$ (surjective). If $\ma...
The goal of this study is to bring out the following conclusion: Let $\mathcal{R}$ be a non-commutative prime ring of characteristic not two and $\mathcal{D}$ be a bi-semiderivation on $\mathcal{R}$ with a function $\mathfrak{f}$ (surjective). If $\mathcal{D}$ acts as an endomorphism or as an anti-endomorphism, then $\mathcal{D} =0$ on $\mathcal{R}$.