Table of Contents
Algebra
Volume 2014 (2014), Article ID 392902, 8 pages
http://dx.doi.org/10.1155/2014/392902
Research Article

Some Properties of Multiplicative -Rings of Polynomials over Multiplicative Hyperrings

Department of Mathematics, Sree Chaitanya College, Habra-Prafullanagar, 24 Parganas (North), West Bengal 743268, India

Received 22 May 2014; Accepted 30 September 2014; Published 27 October 2014

Academic Editor: Andrei V. Kelarev

Copyright © 2014 Utpal Dasgupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Vougiouklis, “The fundamental relation in hyperrings. The general hyperfield,” in Algebraic Hyperstructures and Applications (Xanthi,1990), pp. 203–211, World Science Publisher, Teaneck, NJ, USA, 1991. View at Google Scholar · View at MathSciNet
  2. M. R. Darafsheh and B. Davvaz, “Hv-ring of fractions,” Italian Journal of Pure and Applied Mathematics, no. 5, pp. 25–34, 1999. View at Google Scholar · View at MathSciNet
  3. B. Davvaz and V. Leoreanu-Fotea, Hyperring Theory and Applications, International Academic Press, Palm Harbor, Fla, USA, 2007.
  4. S. Spartalis, A. Dramalides, and T. Vougiouklis, “On Hv-group rings,” Algebras, Groups and Geometries, vol. 15, no. 1, pp. 47–54, 1998. View at Google Scholar · View at MathSciNet
  5. T. Vougiouklis, “Hv-groups defined on the same set,” Discrete Mathematics, vol. 155, no. 1–3, pp. 259–265, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. R. Procesi and R. Rota, “Multiplicative Hv -rings and complementary hyperstructures,” Journal of Discrete Mathematical Sciences & Cryptography, vol. 11, no. 4, pp. 447–456, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. S. Spartalis, “On the number of Hv-rings with P-hyperoperations,” Discrete Mathematics, vol. 155, no. 1–3, pp. 225–231, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. P. Corsini, Prolegomena of Hypergroup Theory, Rivista di Matematica Pura ed Applicata, Aviani, Tricesimo, Italy, 1993.
  9. M. K. Sen and U. Dasgupta, “Some aspects of GH-rings,” Annals of the Alexandru Ioan Cuza University—Mathematics, vol. 56, no. 2, pp. 253–272, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. C. Namnak, N. Triphop, and Y. Kemprasit, “Homomorphisms of some multiplicative hyperrings,” Set-Valued Mathematics and Applications, vol. 1, no. 2, pp. 145–152, 2008. View at Google Scholar
  11. D. M. Olson and V. K. Ward, “A note on multiplicative hyperring,” Italian Journal of Pure and Applied Mathematics, vol. 1, pp. 77–84, 1997. View at Google Scholar · View at MathSciNet
  12. R. Procesi and R. Rota, “Complementary multiplicative hyperrings,” Discrete Mathematics, vol. 308, no. 2-3, pp. 188–191, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. R. Procesi and R. Rota, “On some classes of hyperstructures,” Discrete Mathematics, vol. 208-209, pp. 485–497, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. Rota, “Strongly distributive multiplicative hyperrings,” Journal of Geometry, vol. 39, no. 1-2, pp. 130–138, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. R. Rota, “Sugli Iperanelli Moltiplicativi,” Rendiconti di Matematica, Series VII, vol. 2, no. 4, pp. 711–724, 1982. View at Google Scholar
  16. R. Procesi Ciampi and R. Rota, “Polynomials over multiplicative hyperrings,” Journal of Discrete Mathematical Sciences & Cryptography, vol. 6, no. 2-3, pp. 217–225, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  17. T. Vougiouklis, Hyperstructures and Their Representations, Monographs in Mathematics, Hardonic Press, 1994.
  18. U. Dasgupta, “On prime and primary hyperideals of a multiplicative hyperring,” Analele Stiintifice ale Universitatii Al I Cuza din Iasi—Matematica, vol. 58, no. 1, pp. 19–37, 2012. View at Google Scholar · View at Scopus