Semiprime rings with nilpotent Lie ring of inner derivations

Kamil Kular

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

  • Volume: 13, Issue: 1, page 103-107
  • ISSN: 2300-133X

Abstract

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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

How to cite

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Kamil Kular. "Semiprime rings with nilpotent Lie ring of inner derivations." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13.1 (2014): 103-107. <http://eudml.org/doc/268788>.

@article{KamilKular2014,
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},
author = {Kamil Kular},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Lie rings of derivations; semiprime rings; commutativity theorems; Lie-nilpotency; nilpotency},
language = {eng},
number = {1},
pages = {103-107},
title = {Semiprime rings with nilpotent Lie ring of inner derivations},
url = {http://eudml.org/doc/268788},
volume = {13},
year = {2014},
}

TY - JOUR
AU - Kamil Kular
TI - Semiprime rings with nilpotent Lie ring of inner derivations
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2014
VL - 13
IS - 1
SP - 103
EP - 107
AB - 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
LA - eng
KW - Lie rings of derivations; semiprime rings; commutativity theorems; Lie-nilpotency; nilpotency
UR - http://eudml.org/doc/268788
ER -

References

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  1. [1] N. Argaç, H.G. Inceboz, Derivations of prime and semiprime rings, J. Korean Math. Soc. 46 (2009), no. 5, 997-1005. Cited on 104.[Crossref] Zbl1185.16044
  2. [2] M.J. Atteya, Commutativity results with derivations on semiprime rings, J. Math. Comput. Sci. 2 (2012), no. 4, 853-865. Cited on 104. 
  3. [3] M.N. Daif, H.E. Bell, Remarks on derivations on semiprime rings, Internat. J. Math. Math. Sci. 15 (1992), no. 1, 205-206. Cited on 104.[Crossref] Zbl0746.16029
  4. [4] I.N. Herstein, Noncommutative rings, Carus Mathematical Monographs, 15. Mathematical Association of America, Washington, DC, 1994. Cited on 104. Zbl0177.05801
  5. [5] M. Hongan, A note on semiprime rings with derivation, Internat. J. Math. Math. Sci. 20 (1997), no. 2, 413-415. Cited on 104.[Crossref] Zbl0879.16025

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