On skew derivations as homomorphisms or anti-homomorphisms

Mohd Arif Raza; Nadeem ur Rehman; Shuliang Huang

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 3, page 271-278
  • ISSN: 0010-2628

Abstract

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Let R be a prime ring with center Z and I be a nonzero ideal of R . In this manuscript, we investigate the action of skew derivation ( δ , ϕ ) of R which acts as a homomorphism or an anti-homomorphism on I . Moreover, we provide an example for semiprime case.

How to cite

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Raza, Mohd Arif, Rehman, Nadeem ur, and Huang, Shuliang. "On skew derivations as homomorphisms or anti-homomorphisms." Commentationes Mathematicae Universitatis Carolinae 57.3 (2016): 271-278. <http://eudml.org/doc/286828>.

@article{Raza2016,
abstract = {Let $R$ be a prime ring with center $Z$ and $I$ be a nonzero ideal of $R$. In this manuscript, we investigate the action of skew derivation $(\delta ,\varphi )$ of $R$ which acts as a homomorphism or an anti-homomorphism on $I$. Moreover, we provide an example for semiprime case.},
author = {Raza, Mohd Arif, Rehman, Nadeem ur, Huang, Shuliang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {skew derivation; generalized polynomial identity (GPI); prime ring; ideal; prime rings; generalized derivations; Lie ideals; additive maps; homomorphisms; anti-homomorphisms},
language = {eng},
number = {3},
pages = {271-278},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On skew derivations as homomorphisms or anti-homomorphisms},
url = {http://eudml.org/doc/286828},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Raza, Mohd Arif
AU - Rehman, Nadeem ur
AU - Huang, Shuliang
TI - On skew derivations as homomorphisms or anti-homomorphisms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 3
SP - 271
EP - 278
AB - Let $R$ be a prime ring with center $Z$ and $I$ be a nonzero ideal of $R$. In this manuscript, we investigate the action of skew derivation $(\delta ,\varphi )$ of $R$ which acts as a homomorphism or an anti-homomorphism on $I$. Moreover, we provide an example for semiprime case.
LA - eng
KW - skew derivation; generalized polynomial identity (GPI); prime ring; ideal; prime rings; generalized derivations; Lie ideals; additive maps; homomorphisms; anti-homomorphisms
UR - http://eudml.org/doc/286828
ER -

References

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  1. Asma A., Rehman N., Ali S., 10.1023/B:AMHU.0000003893.61349.98, Acta Math. Hungar. 101 (2003), 79–82. MR2011464DOI10.1023/B:AMHU.0000003893.61349.98
  2. Beidar K.I., Martindale W.S.III, Mikhalev A.V., Rings with Generalized Identities, Pure and Applied Mathematics, 196, Marcel Dekker, New York, 1996. Zbl0847.16001MR1368853
  3. Bell H.E., Kappe L.C., 10.1007/BF01953371, Acta Math. Hungar. 53 (1989), 339–346. Zbl0705.16021MR1014917DOI10.1007/BF01953371
  4. Dhara B., 10.1007/s13366-011-0051-9, Beitr. Algebra Geom. 53 (2012), no. 1, 203–209. Zbl1242.16039MR2890375DOI10.1007/s13366-011-0051-9
  5. Chuang C.L., 10.1090/S0002-9939-1988-0947646-4, Proc. Amer. Math. Soc. 103 (1988), no. 3, 723–728. Zbl0656.16006MR0947646DOI10.1090/S0002-9939-1988-0947646-4
  6. Chuang C.L., 10.1006/jabr.1993.1181, J. Algebra 160 (1993), 291–335. MR1237081DOI10.1006/jabr.1993.1181
  7. Chuang C.L., Lee T.K., 10.1016/j.jalgebra.2003.12.032, J. Algebra 288 (2005), 59–77. Zbl1073.16021MR2138371DOI10.1016/j.jalgebra.2003.12.032
  8. Eremita D., Ilisvic D., 10.3336/gm.47.1.08, Glas. Mat. Ser. III 47 (2012) no. 67, 105–118. MR2942778DOI10.3336/gm.47.1.08
  9. Erickson T.S., Martindale W.S.3rd., Osborn J.M., 10.2140/pjm.1975.60.49, Pacific. J. Math. 60 (1975), 49–63. Zbl0355.17005MR0382379DOI10.2140/pjm.1975.60.49
  10. Gusic I., 10.3336/gm.40.1.05, Glas. Mat. 40 (2005), 47–49. Zbl1072.16031MR2195859DOI10.3336/gm.40.1.05
  11. Jacobson N., Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Providence, Rhode Island, 1964. Zbl0098.25901MR0222106
  12. Kharchenko V.K., Popov A.Z., 10.1080/00927879208824517, Comm. Algebra 20 (1992), 3321–3345. Zbl0783.16012MR1186710DOI10.1080/00927879208824517
  13. Kharchenko V.K., 10.1007/BF01668425, Algebra i Logika 14 (1975), no. 2, 132–148. Zbl0382.16009MR0399153DOI10.1007/BF01668425
  14. Lanski C., 10.1090/S0002-9939-1993-1132851-9, Proc. Amer. Math. Soc. 118 (1993), 75–80. Zbl0869.16027MR1132851DOI10.1090/S0002-9939-1993-1132851-9
  15. Lee P.H., Wong T.L., Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sin. 23 (1995), no. 1–5. Zbl0827.16025MR1319474
  16. Rehman N., 10.3336/gm.39.1.03, Glas. Mat. 39 (2014), 27–30. MR2055383DOI10.3336/gm.39.1.03
  17. Rehman N., Raza M.A., On ideals with skew derivations of prime rings, Miskolc Math. Notes 15 (2014), no. 2, 717-724. Zbl1324.16048MR3302354
  18. Rehman N., Raza M.A., On m -commuting mappings with skew derivations in prime rings, Algebra i Analiz 27 (2015) no. 4, 74–86. Zbl1342.16040
  19. Rehman N., Raza M.A., 10.1016/j.ajmsc.2014.09.001, Arab. Math. J., http://dx.doi.org/10.1016/j.ajmsc.2014.09.001. DOI10.1016/j.ajmsc.2014.09.001
  20. Wang Y., You H., 10.1007/s10114-005-0840-x, Acta. Math. Sinica 23 (2007), 1149-1152. MR2319944DOI10.1007/s10114-005-0840-x

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