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On Posner's second theorem in additively inverse semirings

Year 2019, Volume: 48 Issue: 4, 996 - 1000, 08.08.2019

Abstract

In this paper, we generalize Posner's second theorem in additively inverse semirings. This can be regarded as the generalization of Posner's theorem in semirings.

References

  • [1] R. Awtar, Lie and Jordan Structure in Prime rings with derivations, Proc. Amer. Math. Soc. 41 (1), 67-74, 1973.
  • [2] H.J. Bandlet, M. Petrich, Subdirect products of rings and distrbutive lattics, Proc. Edin Math. Soc. 25, 135-171, 1982.
  • [3] J.S. Golan, The theory of semirings with applications in mathematics and theoretical computer science, John Wiley and Sons. Inc., New York, 1992.
  • [4] M.A. Javed and M. Aslam, Some Commutativity conditions in Prime MA-semirings, ARS Combinatoria 114, 373-384, 2014.
  • [5] M.A. Javed, M. Aslam and M. Hussain, On Condition (A2) of Bandlet and Petrich for inverse semirings, International Mathematical Forum 7, 2903-2914, 2012.
  • [6] P.H. Karvellas, Inversive semirings, J. Aust. Math. Soc. 18, 277-288, 1974.
  • [7] C.P. Lanski, Differential identities, Lie ideals, and Posner’s theorems, Pacific J. Math. 134 (2), 275-297, 1988.
  • [8] L. Oukhtite, Posner’s second theorem for Jordan ideals in Rings with involution, Expo. Math. 29, 415-419, 2011.
  • [9] L. Oukhtite, S. Salhi and L. Taoufiq, Commutativity conditions on Derivations and Lie ideals in σ-Prime Rings, Beiträge Algebra Geom. 51 (1), 275-282, 2010.
  • [10] E.C. Posner, Derivation in Prime Rings, Proc. Amer. Math. Soc. 8, 1093-1100, 1957.
  • [11] S. Sara and M. Aslam, Centralizers on semiprime MA semiring, Quasigroups Related Systems 24, 269-276, 2016.
  • [12] S. Sara and M. Aslam, On Lie ideals of Inverse semirings, accepted in Italian Journal of Pure and Applied Mathematics.
  • [13] S. Sara, M. Aslam and M.A. Javed, On Dependent elements and Free actions in Inverse semirings, International Mathematical Forum 11, 557 - 564, 2016.
  • [14] S. Sara, M.. Aslam and M.A. Javed, On Centralizer of semiprime inverse semirings, Discuss. Math. Gen. Algebra Appl. 36, 71-84, 2016.
  • [15] S. Sara, M. Aslam and M.A. Javed, On Jordan Mappings of inverse semirings, Open Math. 15, 1123-1131, 2017.
  • [16] J. Vukman, Commuting and Centralizing Mappings in Prime Rings, Proc. Amer. Math. Soc. 109 (I), 47- 52, 1990.
Year 2019, Volume: 48 Issue: 4, 996 - 1000, 08.08.2019

Abstract

References

  • [1] R. Awtar, Lie and Jordan Structure in Prime rings with derivations, Proc. Amer. Math. Soc. 41 (1), 67-74, 1973.
  • [2] H.J. Bandlet, M. Petrich, Subdirect products of rings and distrbutive lattics, Proc. Edin Math. Soc. 25, 135-171, 1982.
  • [3] J.S. Golan, The theory of semirings with applications in mathematics and theoretical computer science, John Wiley and Sons. Inc., New York, 1992.
  • [4] M.A. Javed and M. Aslam, Some Commutativity conditions in Prime MA-semirings, ARS Combinatoria 114, 373-384, 2014.
  • [5] M.A. Javed, M. Aslam and M. Hussain, On Condition (A2) of Bandlet and Petrich for inverse semirings, International Mathematical Forum 7, 2903-2914, 2012.
  • [6] P.H. Karvellas, Inversive semirings, J. Aust. Math. Soc. 18, 277-288, 1974.
  • [7] C.P. Lanski, Differential identities, Lie ideals, and Posner’s theorems, Pacific J. Math. 134 (2), 275-297, 1988.
  • [8] L. Oukhtite, Posner’s second theorem for Jordan ideals in Rings with involution, Expo. Math. 29, 415-419, 2011.
  • [9] L. Oukhtite, S. Salhi and L. Taoufiq, Commutativity conditions on Derivations and Lie ideals in σ-Prime Rings, Beiträge Algebra Geom. 51 (1), 275-282, 2010.
  • [10] E.C. Posner, Derivation in Prime Rings, Proc. Amer. Math. Soc. 8, 1093-1100, 1957.
  • [11] S. Sara and M. Aslam, Centralizers on semiprime MA semiring, Quasigroups Related Systems 24, 269-276, 2016.
  • [12] S. Sara and M. Aslam, On Lie ideals of Inverse semirings, accepted in Italian Journal of Pure and Applied Mathematics.
  • [13] S. Sara, M. Aslam and M.A. Javed, On Dependent elements and Free actions in Inverse semirings, International Mathematical Forum 11, 557 - 564, 2016.
  • [14] S. Sara, M.. Aslam and M.A. Javed, On Centralizer of semiprime inverse semirings, Discuss. Math. Gen. Algebra Appl. 36, 71-84, 2016.
  • [15] S. Sara, M. Aslam and M.A. Javed, On Jordan Mappings of inverse semirings, Open Math. 15, 1123-1131, 2017.
  • [16] J. Vukman, Commuting and Centralizing Mappings in Prime Rings, Proc. Amer. Math. Soc. 109 (I), 47- 52, 1990.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sara Shafiq This is me 0000-0001-8838-3875

Muhammad Aslam This is me 0000-0001-9429-625X

Publication Date August 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 4

Cite

APA Shafiq, S., & Aslam, M. (2019). On Posner’s second theorem in additively inverse semirings. Hacettepe Journal of Mathematics and Statistics, 48(4), 996-1000.
AMA Shafiq S, Aslam M. On Posner’s second theorem in additively inverse semirings. Hacettepe Journal of Mathematics and Statistics. August 2019;48(4):996-1000.
Chicago Shafiq, Sara, and Muhammad Aslam. “On Posner’s Second Theorem in Additively Inverse Semirings”. Hacettepe Journal of Mathematics and Statistics 48, no. 4 (August 2019): 996-1000.
EndNote Shafiq S, Aslam M (August 1, 2019) On Posner’s second theorem in additively inverse semirings. Hacettepe Journal of Mathematics and Statistics 48 4 996–1000.
IEEE S. Shafiq and M. Aslam, “On Posner’s second theorem in additively inverse semirings”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, pp. 996–1000, 2019.
ISNAD Shafiq, Sara - Aslam, Muhammad. “On Posner’s Second Theorem in Additively Inverse Semirings”. Hacettepe Journal of Mathematics and Statistics 48/4 (August 2019), 996-1000.
JAMA Shafiq S, Aslam M. On Posner’s second theorem in additively inverse semirings. Hacettepe Journal of Mathematics and Statistics. 2019;48:996–1000.
MLA Shafiq, Sara and Muhammad Aslam. “On Posner’s Second Theorem in Additively Inverse Semirings”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, 2019, pp. 996-1000.
Vancouver Shafiq S, Aslam M. On Posner’s second theorem in additively inverse semirings. Hacettepe Journal of Mathematics and Statistics. 2019;48(4):996-1000.