Authors:
K. Subbarayudu,A. Sivakameshwara Kumar,C. Jaya Subba Reddy,DOI NO:
https://doi.org/10.26782/jmcms.2026.03.00005Keywords:
Semiprime ring,Derivation,Jordan derivation,Generalized derivation,(σ, τ) -derivation,Generalized (σ, τ) -derivation,Jordan (σ, τ) -derivation,Generalized Jordan (σ, τ) - derivation.,Abstract
Let R be a 2-torsion-free semiprime ring, F:R→R be a generalized Jordan (σ,τ)-derivation associated with Jordan (σ,τ)-derivation d, and H:R→R be a left σ-centralizer. If (i) F(x^2 )∓H(x^2 )=0 (ii) F(x^2 )∓H(x^2 )∈C_(σ,τ); for all x,y∈R.Refference:
I. Ashraf M., Rehman N and Shakir Ali: On lie ideals and Jordan generalized derivations of prime rings, Indian J. pure appl. Math. Vol.34,2 (2003), 291-294, ISSN:0019-5588.
II. Awtar R: Lie ideals and Jordan derivations of prime rings, Proc. Amer. math. Soc. Vol.90 (1984), 9-14, ISSN:0002-9939. 10.1090/S0002-9939-1984-0727230-5.
III. Bresar M: Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. Vol.104,(1988), 1003-1006, ISSN: 0002-9939. 10.1090/S0002-9939-1988-0935131-0
IV. Bresar,M and Vukman,J: Jordan derivations on prime rings, Bull. Aust. Math.Soc.,Vol.37,(1988),321-322. ISSN:0004-9727.
10.1017/S0004972700026927
V. Bresar .M and Vukman .J: Jordan (?,?)-derivations, Glasnik Math, Vol. 26,46 (1991), 13- 17, ISSN: 0017-095X. https://hrcak.srce.hr/glasnik-matematicki
VI. Didem,K.C and Neset Aydin: On Multiplicative (generalized)-derivation in semiprime rings, Commun. Fac. Sci. Univ. Auk. Ser. A 1 Math. Stat. Vol 66(1) (2017),153-164,ISSN:1303-5991. 10.1501/Commua1_0000000784.
VII. Herstein.I.N: Jordan derivations of prime rings, Proc. Amer. math. Soc.Vol8,(1957),1104-1110. ISSN: 1088-6826. 10.1090/S0002-9939-1957-0095863-7.
VIII. Herstein,I.N: Topics in ring theory, Univ. of Chicago Press, Chicago, 1969, ISBN: 9780226328010.
IX. Jaya Subba Reddy C., Vasanth Kumar S. and Mallikarjuna Rao S: Prime near rings with generalized Jordan derivations, International journal of Mathematics and Computer Applications Research, Vol.6 (2), (2016), 61-66,ISSN: 2249-6955.
http://www.tjprc.org/journals/journal-details/international-journal-of-mathematics-and-computer-applications-research.
X. Jaya Subba Reddy, C., K. Subbarayudu,. and Mallikarjuna Rao, S: Centralizing with Generalized (?,?)-derivations on semiprime rings, International Journal of Algebra, HIKARI Ltd, Vol. 10, 2016, no. 10, 477 – 490, ISSN: 1312-8868, 10.12988/ija.2016.6859.

