# Reverse Derivations With Invertible Values

## Authors

• Shahed .A. Hamil Department of Mathematics, College of science, University of Baghdad, Baghdad, Iraq
• A. H. Majeed Department of Mathematics, College of science, University of Baghdad, Baghdad, Iraq

## Keywords:

derivation, reverse derivation

## Abstract

this paper, we will prove the following theorem, Let R be a ring with 1 having
a reverse derivation d ≠ 0 such that, for each x R, either d(x) = 0 or d(x) is
invertible 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 ) 2
where char D = 2, d (D) = 0 and
d(x) = 1 + ax for some a in the center Z of D. Furthermore, if 2R ≠ 0 then R = D 2 is
possible if and only if D does not contain all quadratic extensions of Z, the center of
D.

2023-07-02

Mathematics

## How to Cite

Reverse Derivations With Invertible Values. (2023). Iraqi Journal of Science, 55(4B), 1953-1961. https://ijs.uobaghdad.edu.iq/index.php/eijs/article/view/10826

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