Posner's First Theorem for Ideals in Prime Rings

Mohammad Aslam Siddeeque

doi:https://doi.org/10.14445/22315373/IJMTT-V50P541

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 50 | Number 5 | Year 2017 | Article Id. IJMTT-V50P541 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P541

Posner's First Theorem for Ideals in Prime Rings

Mohammad Aslam Siddeeque

Abstract

Posner's first theorem states that if R is a prime ring of characteristic different from two, d1 and d2 are derivations on R such that the iterate d1d2 is also a derivation of R, then at least one of d1, d2 is zero. In the present paper we extend this result for ideals in prime rings of characteristic different from 2.

Keywords

In the present paper we extend this result for ideals in prime rings of characteristic different from 2.

References

[1] I. N. Herstein, Rings with involution, The University of Chicago Press, Chicago, (1976).
[2] M. Breffsar, Centralizing mappings and derivations in prime rings, J. Algebra, 156, (1993), 385 - 394:
[3] M. Mathieu, Posner's second theorem deduced from the first, Proc. Amer. Math. Soc., 114, (1992), 601 - 602.
[4] L. Oukhtite, Posner's second theorem for jordan ideals in rings with involution, Expositiones Mathematicae, 29, (2011), 415 - 419.
[5] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8, (1957), 1093 - 1100.

Citation :

Mohammad Aslam Siddeeque, "Posner's First Theorem for Ideals in Prime Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 5, pp. 249-251, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P541