caa a22 4500 465825451 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112294 doi (NATIONALLICENCE)springer-10.1007/BF02112294 Vukman J. University of Maribor, VEKŠ, Razlagova 14, Y-62000, Maribor, Yugoslavia aut Two results concerning symmetric bi-derivations on prime rings [Elektronische Daten] [J. Vukman] Summary: LetR be a ring. A bi-additive symmetric mappingD(.,.): R × R → R is called a symmetric bi-derivation if, for any fixedy ∈ R, the mappingx → D(x, y) is a derivation. The purpose of this paper is to prove two results concerning symmetric bi-derivations on prime rings. The first result states that, ifD 1 andD 2 are symmetric bi-derivations on a prime ring of characteristic different from two and three such thatD 1(x, x)D 2(x,x) = 0 holds for allx ∈ R, then eitherD 1 = 0 orD 2 = 0. The second result proves that the existence of a nonzero symmetric bi-derivation on a prime ring of characteristic different from two and three, such that [[D(x, x),x],x] ∈ Z(R) holds for allx ∈ R, whereZ(R) denotes the center ofR, forcesR to be commutative. Birkhäuser Verlag, 1990 Primary 16A12 nationallicence Secondary 16A72 nationallicence aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 181-189 0001-9054 40:1<181 1990 40 10 https://doi.org/10.1007/BF02112294 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112294 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vukman J. University of Maribor, VEKŠ, Razlagova 14, Y-62000, Maribor, Yugoslavia aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 181-189 0001-9054 40:1<181 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer