BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks

ansari A Z. On Identities with Additive Mappings in Rings. IJMSI. 2020; 15 (1) :125-133

URL: http://ijmsi.ir/article-1-1051-en.html

URL: http://ijmsi.ir/article-1-1051-en.html

A. Z. Ansari ^{}

begin{abstract}

If $F,D:Rto R$ are additive mappings which satisfy

$F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems.

end{abstract}

Type of Study: Research paper |
Subject:
Special

1. S. Ali, On generalized left derivations in rings and Banach algebras, Aequat. Math., 81, (2011), 209-226. [DOI:10.1007/s00010-011-0070-5]

2. A. Z. Ansari, F. Shujat, Additive mappings satisfying algebraic conditions in rings Rendiconti del Circolo Matematico di Palermo, 63(2), (2014), 211-219. [DOI:10.1007/s12215-014-0153-y]

3. M. Ashraf, S. Ali, On generalized Jordan left derivations in rings, Bull. Korean Math. Soc. 45(2), (2008), 253-261. [DOI:10.4134/BKMS.2008.45.2.253]

4. M. Ashraf, N. Rehman, and A. Z. Ansari, An additive mapping satisfying an algebraic condition in rings with identity, Journal of Advanced Research in Pure Mathematics, 5(2), (2013), 38-45. [DOI:10.5373/jarpm.1333.022712]

5. B. Dhara, R. K. Sharma, On addtive mappings in rings with identity elements, Interenational Mathematical Forum, 4(15), 2009, 727-732.

6. I. N. Herstein, Derivations in prime rings, Proc. Amer. Math. Soc., 8, (1957), 1104-1110. [DOI:10.1090/S0002-9939-1957-0095864-2]

7. I. N. Herstein, Topics in ring theory, Univ. Chicago Press, Chicago, 1969.

8. B. E. Johnson, and A.M. Sinklair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math., 90, (1968), 1068-1073. [DOI:10.2307/2373290]

9. E. C. Posner, Derivations in prime rings, Proc. amer. Math. Soc., (1957), 1093-1100. [DOI:10.1090/S0002-9939-1957-0095863-0]

10. I. M. Singer, and J. Wermer, Derivations on commutative normes spaces, Math. Ann., 129, (1995) 435-460.

11. M.P. Thomos, The image of a derivation is contained in the radical, Annals of Math., 128, (1988), 435-460. [DOI:10.2307/1971432]

12. Vukman, J. Jordan left derivations on semiprime rings, Math. J. Okayama Univ., 39, 1-6 (1997).

13. Vukman, J. On left Jordan derivations on rings and Banach algebras, Aequationes Math, 75, (2008), 260-266. [DOI:10.1007/s00010-007-2872-z]

14. Zalar, B. On centralizers of semiprime rings, Comment. Math. Univ. carolin., 32(4), (1991) 609-614.