Posner's First Theorem for Ideals in Prime Rings

	International Journal of Mathematics Trends and Technology (IJMTT)
	© 2017 by IJMTT Journal
	Volume-50 Number-5
	Year of Publication : 2017
	Authors : Mohammad Aslam Siddeeque
	10.14445/22315373/IJMTT-V50P541

Mohammad Aslam Siddeeque "Posner's First Theorem for Ideals in Prime Rings ", International Journal of Mathematics Trends and Technology (IJMTT). V50(5):249-251 October 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

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.

Reference
[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.

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