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.
[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.
[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
[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.
[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.
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.