Research Article
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Year 2020, Volume 28, Issue 28, 127 - 140, 14.07.2020
https://doi.org/10.24330/ieja.768202

Abstract

References

  • S. Ali and S. Huang, On derivations in semiprime rings, Algebr. Represent. Theory, 15(6) (2012), 1023-1033.
  • M. Ashraf and M. A. Quadri, Some conditions for the commutativity of rings, Acta Math. Hungar., 61(1-2) (1993), 73-77.
  • M. Ashraf and N. Rehman, On commutativity of rings with derivations, Results Math., 42(1-2) (2002), 3-8.
  • H. E. Bell, Some results on commutativity and anti-commutativity in rings, Acta Math. Hungar., 63(2) (1994), 113-117.
  • H. E. Bell, A. Boua and L. Oukhtite, Semigroup ideals and commutativity in 3-prime near rings, Comm. Algebra, 43(5) (2015), 1757-1770.
  • H. E. Bell and M. N. Daif, On commutativity and strong commutativity-preserving maps, Canad. Math. Bull., 37(4) (1994), 443-447.
  • H. E. Bell and M. N. Daif, On derivations and commutativity in prime rings, Acta Math. Hungar., 66(4) (1995), 337-343.
  • H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull., 30(1) (1987), 92-101.
  • M. Bresar, Commuting traces of biadditive mapping, commutativity preserving mapping and Lie mappings, Trans. Amer. Math. Soc., 335(2) (1993), 525-546.
  • M. Bresar, On the distance of the composition of two derivations to the generalized derivation, Glasgow Math. J., 33(1) (1991), 89-93.
  • M. Bresar and C. R. Miers, Strong commutativity preserving maps of semiprime rings, Canad. Math. Bull., 37(4) (1994), 457-460.
  • V. De Filippis, A. Mamouni and L. Oukhtite, Generalized Jordan semiderivations in prime rings, Canad. Math. Bull., 58(2) (2015), 263-270.
  • Q. Deng and M. Ashraf, On strong commutativity preserving mappings, Results Math., 30 (1996), 259-263.
  • N. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canada Sect. III, 49 (1955), 19-22.
  • A. Fosner, X.-F. Liang and F. Wei, Centralizing traces with automorphisms on triangular algebras, Acta Math. Hungar., 154(2) (2018), 315-342.
  • A. Mamouni, B. Nejjar and L. Oukhtite, Differential identities on prime rings with involution, J. Algebra Appl., 17(9) (2018), 1850163 (11 pp).
  • A. Mamouni, L. Oukhtite and B. Nejjar, On $\ast$-semiderivations and $\ast$-generalized semiderivations, J. Algebra Appl., 16(4) (2017), 1750075 (8 pp).
  • B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Commutativity theorems in rings with involution, Comm. Algebra, 45(2) (2017), 698-708.
  • L. Oukhtite, Posner's second theorem for Jordan ideals in rings with involution, Expo. Math., 29(4) (2011), 415-419.
  • L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math., 38(2) (2014), 225-232.
  • E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
  • P. Semrl, Commutativity preserving maps, Linear Algebra Appl., 429 (2008), 1051-1070.

ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION

Year 2020, Volume 28, Issue 28, 127 - 140, 14.07.2020
https://doi.org/10.24330/ieja.768202

Abstract

In this paper we present some commutativity theorems for prime rings $R$ with involution $\ast$ of the second kind in which endomorphisms satisfy certain algebraic identities. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • S. Ali and S. Huang, On derivations in semiprime rings, Algebr. Represent. Theory, 15(6) (2012), 1023-1033.
  • M. Ashraf and M. A. Quadri, Some conditions for the commutativity of rings, Acta Math. Hungar., 61(1-2) (1993), 73-77.
  • M. Ashraf and N. Rehman, On commutativity of rings with derivations, Results Math., 42(1-2) (2002), 3-8.
  • H. E. Bell, Some results on commutativity and anti-commutativity in rings, Acta Math. Hungar., 63(2) (1994), 113-117.
  • H. E. Bell, A. Boua and L. Oukhtite, Semigroup ideals and commutativity in 3-prime near rings, Comm. Algebra, 43(5) (2015), 1757-1770.
  • H. E. Bell and M. N. Daif, On commutativity and strong commutativity-preserving maps, Canad. Math. Bull., 37(4) (1994), 443-447.
  • H. E. Bell and M. N. Daif, On derivations and commutativity in prime rings, Acta Math. Hungar., 66(4) (1995), 337-343.
  • H. E. Bell and W. S. Martindale, III, Centralizing mappings of semiprime rings, Canad. Math. Bull., 30(1) (1987), 92-101.
  • M. Bresar, Commuting traces of biadditive mapping, commutativity preserving mapping and Lie mappings, Trans. Amer. Math. Soc., 335(2) (1993), 525-546.
  • M. Bresar, On the distance of the composition of two derivations to the generalized derivation, Glasgow Math. J., 33(1) (1991), 89-93.
  • M. Bresar and C. R. Miers, Strong commutativity preserving maps of semiprime rings, Canad. Math. Bull., 37(4) (1994), 457-460.
  • V. De Filippis, A. Mamouni and L. Oukhtite, Generalized Jordan semiderivations in prime rings, Canad. Math. Bull., 58(2) (2015), 263-270.
  • Q. Deng and M. Ashraf, On strong commutativity preserving mappings, Results Math., 30 (1996), 259-263.
  • N. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canada Sect. III, 49 (1955), 19-22.
  • A. Fosner, X.-F. Liang and F. Wei, Centralizing traces with automorphisms on triangular algebras, Acta Math. Hungar., 154(2) (2018), 315-342.
  • A. Mamouni, B. Nejjar and L. Oukhtite, Differential identities on prime rings with involution, J. Algebra Appl., 17(9) (2018), 1850163 (11 pp).
  • A. Mamouni, L. Oukhtite and B. Nejjar, On $\ast$-semiderivations and $\ast$-generalized semiderivations, J. Algebra Appl., 16(4) (2017), 1750075 (8 pp).
  • B. Nejjar, A. Kacha, A. Mamouni and L. Oukhtite, Commutativity theorems in rings with involution, Comm. Algebra, 45(2) (2017), 698-708.
  • L. Oukhtite, Posner's second theorem for Jordan ideals in rings with involution, Expo. Math., 29(4) (2011), 415-419.
  • L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math., 38(2) (2014), 225-232.
  • E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100.
  • P. Semrl, Commutativity preserving maps, Linear Algebra Appl., 429 (2008), 1051-1070.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

L. OUKHTITE This is me (Primary Author)
University S. M. Ben Abdellah
Morocco


H. EL MIR This is me
University S. M. Ben Abdellah
Morocco


B. NEJJAR This is me
University Ibn Tofail
Morocco

Publication Date July 14, 2020
Published in Issue Year 2020, Volume 28, Issue 28

Cite

Bibtex @research article { ieja768202, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {127 - 140}, doi = {10.24330/ieja.768202}, title = {ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION}, key = {cite}, author = {Oukhtıte, L. and El Mır, H. and Nejjar, B.} }
APA Oukhtıte, L. , El Mır, H. & Nejjar, B. (2020). ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION . International Electronic Journal of Algebra , 28 (28) , 127-140 . DOI: 10.24330/ieja.768202
MLA Oukhtıte, L. , El Mır, H. , Nejjar, B. "ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION" . International Electronic Journal of Algebra 28 (2020 ): 127-140 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768202>
Chicago Oukhtıte, L. , El Mır, H. , Nejjar, B. "ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION". International Electronic Journal of Algebra 28 (2020 ): 127-140
RIS TY - JOUR T1 - ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION AU - L.Oukhtıte, H.El Mır, B.Nejjar Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768202 DO - 10.24330/ieja.768202 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 127 EP - 140 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768202 UR - https://doi.org/10.24330/ieja.768202 Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Algebra ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION %A L. Oukhtıte , H. El Mır , B. Nejjar %T ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768202 %U 10.24330/ieja.768202
ISNAD Oukhtıte, L. , El Mır, H. , Nejjar, B. . "ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION". International Electronic Journal of Algebra 28 / 28 (July 2020): 127-140 . https://doi.org/10.24330/ieja.768202
AMA Oukhtıte L. , El Mır H. , Nejjar B. ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION. IEJA. 2020; 28(28): 127-140.
Vancouver Oukhtıte L. , El Mır H. , Nejjar B. ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION. International Electronic Journal of Algebra. 2020; 28(28): 127-140.
IEEE L. Oukhtıte , H. El Mır and B. Nejjar , "ENDOMORPHISMS WITH CENTRAL VALUES ON PRIME RINGS WITH INVOLUTION", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 127-140, Jul. 2020, doi:10.24330/ieja.768202