International Journal of Modern Computation, Information and Communication Technology
December 2018, Vol. 1, Issue 7, p. 121-125.
Characterizations of Derivations on Prime Rings
Kaunda C. Matoke, Donald Odongo, N. B. Okelo*
School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo-Kenya.
*Corresponding author’s e-mail: bnyaare@yahoo.com
Abstract
In the present paper, we have studied a (α,α)-symmetric derivations D on semiprime rings and prime rings R, we give some results when R admits a (α,α)-symmetric derivations D to satisfy some conditions on R.(i)D([x,y]n+1) =0 for all x, y∈ R. (ii) [D(xn+1),α(y)] = 0 for all x, y ∈R. (iii) [[D(x),α(x)],α(x)]= 0 for all x ∈R. Where α: R →R is an automorphism mapping.
Keywords: Semiprime Ring; Prime Ring; (α,α)-Derivations; (α,α)-Symmetric Derivation.
References
- Ali A. Ideals and symmetric (σ,σ)-biderivations on prime rings. Aligarh Bull Math 2017;25:9-18.
- Andrijevic D. On b-open sets. Mat Vesnik 1996;48:59-64.
- Brooks F. Indefinite cut sets for real functions. Amer Math Monthly 1971;78:1007-10.
- Chinnadurai V, Bharathivelan K. Cubic Ideals in Near Subtraction Semigroups. Int J Mod Sci Technol 2016;1(8):276-82.
- Ekici E. On contra-continuity. Annales Univ Sci Bodapest 2004;47:127-37.
- Ekici E. New forms of contra-continuity, Carpathian J Math 2008; 24(1): 37-45.
- Herstein IN. A note on derivations. Canad Math Bull 2018;21:369-70.
- Katˇetov M. On real-valued functions in topological spaces. Fund Math 1951;38:85-91.
- Lane E. Insertion of a continuous function. Pacific J Math 1976;66:181-90.
- Maheshwari SN, Prasad R.On ROs-spaces. Portugal Math 1975;34:213-17.
- Okelo NB. On characterization of various finite subgroups of Abelian groups. Int J Mod Comp Inform Commun Technol 2018;1(5):93-8
- Vijayabalaji S, Sathiyaseelan N. IntervalValued Product Fuzzy Soft Matrices and its Application in Decision Making. Int J Mod Sci Technol 2016;1(7):159-63.
- Vukman J. Derivations on semiprime rings. Bull Austral Math Soc 2016;53:353-59.