DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

Sara Shafiq

Sara Shafiq

Lahore College for Women University Lahore

email: saro_c18@yahoo.com

R. Uzma

R. Uzma

Department of Mathematics
LCWU, Lahore, Pakistan

email: ramzanu16@gmail.com

Title:

Some results on dependent elements in semirings

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2022-06-24 , Revised: 2022-10-25 , Accepted: 2022-10-25 , Available online: 2023-11-13 , https://doi.org/10.7151/dmgaa.1445

Abstract:

In this paper, we introduce the notion of dependent elements of derivation in MA-Semirings. We also generalize some results of dependent elements of derivation of rings for MA-Semiring.

Keywords:

MA-semiring, semiprime MA-semiring, commutators, centralizer, derivation, dependent element, free action

References:

  1. Ali, F. and Chaudhry, M. A. Dependent elements of derivations on semiprime rings. International Journal of Mathematics and Mathematical Sciences, (2009). https://doi.org/10.1155/2009/696737
  2. Bandelt, H. J. and Petrich, M. Subdirect products of rings and distributive lattices. Proceedings of the Edinburgh Mathematical Society, 25(2): 155-171 (1982).https://doi.org/10.1017/s0013091500016643
  3. Chaudhry, M. A. and Samman, M. S. Free actions on semiprime rings. Mathematica Bohemica, 133(2): 197-208 (2008). https://doi.org/10.21136/mb.2008.134055
  4. Golan, J. The Theory of Semirings with Application in Math. and Theoretical Computer Science, (Vol. 54), Monographs and Surveys in Pure and Applied Mathematics. (1992).
  5. Javed, M. A. and Aslam, M. Some commutativity conditions in prime MA-semirings. ARS COMBINATORIA, 114: 373-384 (2014).
  6. Javed, M. A., Aslam, M. and Hussain, M. On condition (A2) of Bandlet and Petrich for inverse semirings. In Int. Math. Forum, 7(59): 2903-2914 (2012).
  7. Kallman, R. R. A generalization of free action. Duke Mathematical Journal, 36(4): 781-789 (1969). http://gdmltest.u-ga.fr/item/1077378641/
  8. Karvellas, P. H. Inversive semirings. Journal of the Australian Mathematical Society, 18(3): 277-288 (1974).https://doi.org/10.1215/s0012-7094-69-03693-x
  9. Murray, F. J. and von Neumann, J. On rings of operators. II. Transactions of the American Mathematical Society, 41(2): 208-248 (1937).
  10. Murugesan, R., Sindhu, K. K. and Namasivayam, P. Free Actions of Semi derivations on Semiprime Semirings. International Journal of Science and Engineering Invention, 2(04): (2016).
  11. Sara, S., Aslam, M. and Javed, M. A. On dependent elements and free actions in inverse semirings. In Int. Math. Forum, 12: 557-564 (2016).https://doi.org/10.12988/imf.2016.6441
  12. Sara, S., Aslam, M. and Javed, M. On centralizer of semiprime inverse semiring. Discussiones Mathematicae-General Algebra and Applications, 36(1): 71-84 (2016).https://doi.org/10.7151/dmgaa.1252
  13. S. Sara and M. Aslam, On Posners Second theorem in additively inverse semiring, Hacettepe Journal of Mathematics and Statistics, 48(4) (2019), 996-1000. https://doi.org/10.15672/hjms.2018.576
  14. S. Sara and M. Aslam, On Lie ideals of Inverse Semirings, Italian Journal of Pure and Applied Mathematics, 44 (2020), 22-29. https://doi.org/10.1142/s1793557121501813
  15. Thaheem, A. On dependent elements in semiprime rings. Mathematica Japonicae, 47(1): 29-31 (1998).
  16. Vukman, J. and Kosi-Ulbl, I. On dependent elements in rings. International Journal of Mathematics and Mathematical Sciences, 54: 2895-2906 (2004).https://doi.org/10.1155/s0161171204311221
Close