Derivable Maps of Prime Rings - Mahdi, Huda; Majeed, A. (Iraqi Journal of Science, 2023)
Our active aim in this paper is to prove the following Let Ŕ be a ring having anidempotent element e(e  0,e 1) . Suppose that R is a subring of Ŕ whichsatisfies:(i) eR  R and Re  R .(ii) xR  0 implies x  0 .(iii ) eRx  0 implies x  0( and hence Rx  0 implies x  0) .(iv) exeR(1 e)  0 implies exe  0 .If D is a derivable map of R satisfying D(R )  R ;i, j 1,2. ij ij Then D isadditive. This extend Daif's result to the case R need not contain any non-zeroidempotent element.