id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-828	Saed, I. A.	(,)- Strongly Derivations Pairs on Rings	2016	10	.pdf	application/pdf	2654	152	87	Definition 2.1 Let R be a ring, additive mappings d,g : RR is called (,)-S-derivation pair (d,g) where , : RR are two mappings of R, if satisfy the following equations: d(xy)=d(x)σ(y) + (x)g(y), for all x,y  R. g(xy)=g(x)σ(y) + (x)d(y), for all x,y  R. And is called Jordan (,)-S-derivation pair if: d(x 2)=d(x)σ(x) + (x)g(x), for all x  R. g(x2)=g(x)σ(x) + (x)d(x), for all x  R. The following example explains the principle definition: Example 2.2 Let R be a non commutative ring and let a,b  R, such that (x) a= (x)b = 0, for all x  R. Define d,g: R  R as follows: d(x) = a (x), g(x) = b (x), for all x  R where , : R  R. Define an additive pair d,g: R  R, as follows: d(x) = (x) a + a (x), g(x)	cache/iajs-828.pdf	txt/iajs-828.txt