On Jordan ideals and derivations in rings with involution

Lahcen Oukhtite

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 3, page 389-395
  • ISSN: 0010-2628

Abstract

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Let R be a 2 -torsion free * -prime ring, d a derivation which commutes with * and J a * -Jordan ideal and a subring of R . In this paper, it is shown that if either d acts as a homomorphism or as an anti-homomorphism on J , then d = 0 or J ⊆ Z ( R ) . Furthermore, an example is given to demonstrate that the * -primeness hypothesis is not superfluous.

How to cite

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Oukhtite, Lahcen. "On Jordan ideals and derivations in rings with involution." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 389-395. <http://eudml.org/doc/38135>.

@article{Oukhtite2010,
abstract = {Let $R$ be a $2$-torsion free $\ast $-prime ring, $d$ a derivation which commutes with $\ast $ and $J$ a $\ast $-Jordan ideal and a subring of $R$. In this paper, it is shown that if either $d$ acts as a homomorphism or as an anti-homomorphism on $J$, then $d=0$ or $J\subseteq Z(R)$. Furthermore, an example is given to demonstrate that the $\ast $-primeness hypothesis is not superfluous.},
author = {Oukhtite, Lahcen},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\ast $-prime rings; Jordan ideals; derivations; *-prime rings; Jordan ideals; derivations; homomorphisms; anti-homomorphisms},
language = {eng},
number = {3},
pages = {389-395},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Jordan ideals and derivations in rings with involution},
url = {http://eudml.org/doc/38135},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Oukhtite, Lahcen
TI - On Jordan ideals and derivations in rings with involution
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 389
EP - 395
AB - Let $R$ be a $2$-torsion free $\ast $-prime ring, $d$ a derivation which commutes with $\ast $ and $J$ a $\ast $-Jordan ideal and a subring of $R$. In this paper, it is shown that if either $d$ acts as a homomorphism or as an anti-homomorphism on $J$, then $d=0$ or $J\subseteq Z(R)$. Furthermore, an example is given to demonstrate that the $\ast $-primeness hypothesis is not superfluous.
LA - eng
KW - $\ast $-prime rings; Jordan ideals; derivations; *-prime rings; Jordan ideals; derivations; homomorphisms; anti-homomorphisms
UR - http://eudml.org/doc/38135
ER -

References

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  1. Ashraf M., Ali A., Rehman N., 10.1023/B:AMHU.0000003893.61349.98, Acta Math. Hungar. 101 (2003), 79–82. MR2011464DOI10.1023/B:AMHU.0000003893.61349.98
  2. Bell H.E., Kappe L.C., 10.1007/BF01953371, Acta Math. Hungar. 53 (1989), 339–346. Zbl0705.16021MR1014917DOI10.1007/BF01953371
  3. Oukhtite L., Salhi S., Taoufiq L., σ -Lie ideals with derivations as homomorphisms and anti-homomorphisms, Int. J. Algebra 1 (2007), no. 5, 235–239. Zbl1124.16028MR2342996
  4. Oukhtite L., Salhi S., On generalized derivations of σ -prime rings, Afr. Diaspora J. Math. 5 (2007), no. 1, 21–25. MR2337187
  5. Zaidi S.M.A., Ashraf M., Ali S., 10.1155/S0161171204309075, Int. J. Math. Math. Sci. 2004 (2004), no. 37–40, 1957–1964. Zbl1069.16041MR2100888DOI10.1155/S0161171204309075
  6. Posner E.C., 10.1090/S0002-9939-1957-0095863-0, Proc. Amer. Math. Soc. 8 (1957), 1093–1100. Zbl0082.03003MR0095863DOI10.1090/S0002-9939-1957-0095863-0

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