The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

ON ISOMORPHISM THEOREMS AND CHINESE REMAINDER THEOREM IN HYPERNEAR RINGS

  • M. Al Tahan (Department of Mathematics and Statistics, Abu Dhabi University) ;
  • B. Davvaz (Department of Mathematical Sciences, Yazd University)
  • Received : 2023.03.19
  • Accepted : 2023.05.27
  • Published : 2023.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this paper is to consider the abstract theory of hypernear rings. In this regard, we derive the isomorphism theorems for hypernear rings as well as Chinese Remainder theorem. Our results can be considered as a generalization for the cases of Krasner hyperrings, near rings and rings.

Keywords

References

  1. J. Clay: Near-rings: Geneses and Applications. Oxford, New York, 1992. 
  2. S.D. Comer: Polygroups derived from cogroups. J. Algebra 89 (1984), 397-405. https://doi.org/10.1016/0021-8693(84)90225-4 
  3. B. Davvaz: Polygroup Theory and Related Systems. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. viii+200 pp. 
  4. B. Davvaz & A. Salasi: A realization of hyperring. Communication in Algebra 34 (2006), no. 12, 4389-4400. https://doi.org/10.1080/00927870600938316 
  5. V. Dasic: Hypernear-rings. Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (AHA 1990), Word Scientific, (1991), 75-85. 
  6. L. Dickson: Definitions of a group and a field by independent postulates. Trans. Amer. Math. Soc. 6 (1905), 198-204. https://doi.org/10.2307/1986446 
  7. G. Ferrero & C. Ferrero-Cotti: Nearrings. Some Developments Linked to Semigroups and Groups. Kluwer, Dordrecht, 2002. 
  8. V.M. Gontineac: On hypernear-rings and H-hypergroups. Proc. Fifth Int. Congress on Algebraic Hyperstructures and Applications (AHA 1993), Hadronic Press, Inc., USA, (1994) 171-179. 
  9. M. Krasner: A Class of Hyperrings and Hyperfields. Internat. J. Math. and Math. Sci. 6 (1983), no. 2, 307-312. https://doi.org/10.1155/S0161171283000265 
  10. F. Marty: Sur une generalization de la notion de group. In 8th Congress Math. Scandenaves, (1934), pp. 45-49.