Geodesic
Commutativity of Prime Rings with Symmetric Biderivations
Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 2, pp. 221-226.

Voir la notice de l'article provenant de la source Library of Science

The present paper shows some results on the commutativity of R: Let R be a prime ring and for any nonzero ideal I of R, if R admits a biderivation B such that it satisfies any one of the following properties (i) B([x, y], z) = [x, y], (ii) B([x, y], m) + [x, y] = 0, (iii) B(xoy, z) = xoy, (iv) B(xoy, z) + xoy = 0, (v) B(x, y)oB(y, z) = 0, (vi)B(x, y)oB(y, z) = xoz, (vii) B(x, y)oB(y, z) + xoy = 0, for all x, y, z ∈ R, then R is a commutative ring.
Keywords: prime ring, biderivation, commutativity and ideals 
@article{DMGAA_2018_38_2_a4,
     author = {Ramoorthy Reddy, B. and Jaya Subba Reddy, C.},
     title = {Commutativity of {Prime} {Rings} with {Symmetric} {Biderivations}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {221--226},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2018_38_2_a4/}
}
TY  - JOUR
AU  - Ramoorthy Reddy, B.
AU  - Jaya Subba Reddy, C.
TI  - Commutativity of Prime Rings with Symmetric Biderivations
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2018
SP  - 221
EP  - 226
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2018_38_2_a4/
LA  - en
ID  - DMGAA_2018_38_2_a4
ER  - 
%0 Journal Article
%A Ramoorthy Reddy, B.
%A Jaya Subba Reddy, C.
%T Commutativity of Prime Rings with Symmetric Biderivations
%J Discussiones Mathematicae. General Algebra and Applications
%D 2018
%P 221-226
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2018_38_2_a4/
%G en
%F DMGAA_2018_38_2_a4
Ramoorthy Reddy, B.; Jaya Subba Reddy, C. Commutativity of Prime Rings with Symmetric Biderivations. Discussiones Mathematicae. General Algebra and Applications, Tome 38 (2018) no. 2, pp. 221-226. http://geodesic.mathdoc.fr/item/DMGAA_2018_38_2_a4/

[1] M. Ashraf and N.U. Rehman, On commutativity of rings with derivations, Result. Math. 42 (2002) 03–08.

[2] M. Ashraf and N.U. Rehman, On derivation and commutativity in prime rings, East-West J. Math. 3 (2001) 87–91.

[3] M. Atteya and D. Resan, Commuting derivations of semiprime rings, Int. J. Math. Sci. 6 (2011) 1151–1158.

[4] H.E. Bell and M.N. Daif, On derivations and commutativity in prime rings, Acta Math. Hungar. 66 (1995) 337–343.

[5] H.E. Bell and W.S. Martindale, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987) 92–101.

[6] I.N. Herstein, A note on derivations, Canad. Math. Bull. 21 (1978) 369–370. doi:10.4153/CMB-1978-065-x

[7] T.K. Lee, Derivations and centralizing mappings in prime rings, Taiwanese. J. Math. 1 (1997) 333–342.

[8] G. Maksa, On the trace of symmetric biderivations, C.R. Math. Rep. Sci. Canada 9 (1987) 302–307.

[9] J.H. Mayne, Centralizing mappings of prime rings, Canad. Math. Bull. 27 (1984) 122–126. doi:10.4153/CMB-1984-018-2

[10] E.C. Posner, Derivations in prime ring, Proc. Amer. Math. Soc. 8 (1957) 1093–1100.

[11] J. Vukman, Symmetric biderivations on prime and semi prime rings, Aequationes. Math. 38 (1989) 245–254.

[12] J. Vukman, Two results concerning symmetric biderivations on prime rings, Aequationes. Math. 40 (1990) 181–189.

[13] M.S. Yenigul and N. Argac, Ideals and symmetric biderivations on prime and semiprime rings, Math. J. Okayama Univ. 35 (1993) 189–192.