Commutativity theorems for rings with differential identities on Jordan ideals

L. Oukhtite; A. Mamouni; Mohammad Ashraf

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 4, page 447-457
  • ISSN: 0010-2628

Abstract

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In this paper we investigate commutativity of ring R with involution ' * ' which admits a derivation satisfying certain algebraic identities on Jordan ideals of R . Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

How to cite

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Oukhtite, L., Mamouni, A., and Ashraf, Mohammad. "Commutativity theorems for rings with differential identities on Jordan ideals." Commentationes Mathematicae Universitatis Carolinae 54.4 (2013): 447-457. <http://eudml.org/doc/260749>.

@article{Oukhtite2013,
abstract = {In this paper we investigate commutativity of ring $R$ with involution $^\{\prime \}\ast ^\{\prime \}$ which admits a derivation satisfying certain algebraic identities on Jordan ideals of $R$. Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.},
author = {Oukhtite, L., Mamouni, A., Ashraf, Mohammad},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {derivation; generalized derivation; $*$-Jordan ideal; commutativity theorems; differential identities; derivations; prime rings; involutions; Jordan ideals; commutativity theorems},
language = {eng},
number = {4},
pages = {447-457},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Commutativity theorems for rings with differential identities on Jordan ideals},
url = {http://eudml.org/doc/260749},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Oukhtite, L.
AU - Mamouni, A.
AU - Ashraf, Mohammad
TI - Commutativity theorems for rings with differential identities on Jordan ideals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 4
SP - 447
EP - 457
AB - In this paper we investigate commutativity of ring $R$ with involution $^{\prime }\ast ^{\prime }$ which admits a derivation satisfying certain algebraic identities on Jordan ideals of $R$. Some related results for prime rings are also discussed. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.
LA - eng
KW - derivation; generalized derivation; $*$-Jordan ideal; commutativity theorems; differential identities; derivations; prime rings; involutions; Jordan ideals; commutativity theorems
UR - http://eudml.org/doc/260749
ER -

References

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  2. Bell H.E., Daif M.N., 10.1007/BF01876049, Acta Math. Hungar. 66 (1995), 337–343. Zbl0822.16033MR1314011DOI10.1007/BF01876049
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  5. Herstein I.N., 10.4153/CMB-1978-065-x, Canad. Math. Bull. 21 (1978), 369–370. Zbl0434.16027MR0506447DOI10.4153/CMB-1978-065-x
  6. Hongan M., 10.1155/S0161171297000562, Internat. J. Math. Math. Sci. 20 (1997), no. 2, 413–415. Zbl0879.16025MR1444747DOI10.1155/S0161171297000562
  7. Mamouni A., Oukhtite L., 10.1007/s40065-012-0039-9, Arab. J. Math. 1 (2012), no. 3, 341–346. MR3041071DOI10.1007/s40065-012-0039-9
  8. Mamouni A., Oukhtite L., Generalized derivations centralizing on Jordan ideals of rings with involution, submitted. 
  9. Oukhtite L., On Jordan ideals and derivations in rings with involution, Comment. Math. Univ. Carolin. 51 (2010), no. 3, 389–395. Zbl1211.16037MR2741872
  10. Oukhtite L., 10.1016/j.exmath.2011.07.002, Expo. Math. 29 (2011), 415–419. Zbl1232.16027MR2861767DOI10.1016/j.exmath.2011.07.002
  11. Oukhtite L., Salhi S., On derivations in σ -prime rings, Int. J. Algebra 1 (2007), no. 5, 241–246. Zbl1124.16025MR2342997
  12. Zaidi S.M.A., Ashraf A., Ali S., 10.1155/S0161171204309075, Int. J. Math. Math. Sci. 2004, no. 37–40, 1957–1964. Zbl1069.16041MR2100888DOI10.1155/S0161171204309075

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