Some results in semiprime rings with derivation

Yıl 2013, Cilt: 62 Sayı: 1, 11 - 20, 01.02.2013

Emine Koç

https://doi.org/10.1501/Commua1_0000000682

Öz

Some results in semiprime rings with derivation

Öz

Let R be a semiprime ring and S be a nonempty subset of R: A
mapping F from R to R is called centralizing on S if [F(x); x] 2 Z for all
x 2 S. The mapping F is called strong commutativity preserving (SCP) on
S if [F(x); F(y)] = [x; y] for all x; y 2 S: In the present paper, we investigate
some relationships between centralizing derivations and SCP-derivations of
semiprime rings. Also, we study centralizing properties derivation which acts
homomorphism or anti-homomorphism in semiprime rin

Anahtar Kelimeler

Semiprime rings, derivations, centralizing mappings, scp maps

Kaynakça

• A. Ali, M. Yasen and M. Anwar, Strong commutativity preserving mappings on semiprime rings, Bull. Korean Math. Soc., 2006, 43(4), 711-713.
• E. C. Posner, Derivations in prime rings, Proc. Amer. Soc., 1957, 8, 1093-1100.
• H. E. Bell, M. N. Daif, On commutativity and strong commutativity preserving maps, Canad. Math. Bull., 1994, 37(4), 443-447.
• H. E. Bell, L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungarica, 1989, 53, 339-346, .
• H. E. Bell, W. S. Martindale, Centralizing mappings of semiprime rings, Canad. Math. Bull., , 30 (1), 92-101. I.N. Herstein, Rings with involution, The University of Chicago Press, Illinois, 1976.
• J. Ma, X. W. Xu, Strong commutativity-preserving generalized derivations on on semiprime rings, Acta Math. Sinica, English Series, 2008, 24(11), 1835-1842.
• M. Bresar, Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings,. Trans. Amer. Math. Soc., 1993, 335(2), 525-546.
• M. N. Daif, H. E. Bell, Remarks on derivations on semiprime rings, Internat J. Math. Math. Sci., 1992, 15(1), 205-206.
• M.S. Samman, On strong commutativity-preserving maps, Internat J. Math. Math. Sci., 2005, , 917-923.
• N. Argaç, On prime and semiprime rings with derivations, Algebra Colloq., 2006, 13(3), 380.