Reverse Derivations With Invertible Values - .A. Hamil, Shahed; Majeed, A. H. (Iraqi Journal of Science, 2023)
this paper, we will prove the following theorem, Let R be a ring with 1 havinga reverse derivation d ≠ 0 such that, for each x R, either d(x) = 0 or d(x) isinvertible in R, then R must be one of the following: (i) a division ring D, (ii) D 2 ,the ring of 2×2 matrices over D, (iii) D[x]/(x ) 2where char D = 2, d (D) = 0 andd(x) = 1 + ax for some a in the center Z of D. Furthermore, if 2R ≠ 0 then R = D 2 ispossible if and only if D does not contain all quadratic extensions of Z, the center ofD.