Semiprime rings with nilpotent Lie ring of inner derivations

Kamil Kular

Abstract


We give an elementary and self-contained proof of the theorem which says that for a semiprime ring commutativity, Lie-nilpotency, and nilpotency of the Lie ring of inner derivations are equivalent conditions.

Keywords


semiprime ring; nilpotent Lie ring; commutativity; inner derivation

Mathematics Subject Classification (2010)


16W10; 16N60; 16W25

References


Argaç, N. and H.G. Inceboz. "Derivations of prime and semiprime rings." J. Korean Math. Soc. 46.5 (2009): 997-1005.

Atteya, M.J. "Commutativity results with derivations on semiprime rings." J. Math. Comput. Sci. 2.4 (2012): 853-865.

Daif, M.N. and H.E. Bell. "Remarks on derivations on semiprime rings." Internat. J. Math. Math. Sci. 15.1 (1992): 205-206.

Herstein, I.N. "Noncommutative rings." Carus Mathematical Monographs, 15. Washington, DC: Mathematical Association of America, 1994.

Hongan, M. "A note on semiprime rings with derivation." Internat. J. Math. Math. Sci. 20.2 (1997): 413-415.


Full Text: PDF

Download statistics: 2060

Licencja Creative Commons
This article by Kamil Kular is governed by the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej