On Prime Hyperideals of a Krasner Hyperring

On Prime Hyperideals of a Krasner Hyperring

The basis of this study, which was put forth in order to appropriate a special area in the hyperring theory, which has recently been studied as a generalization of the ring theory, which uses the module theory as an application field, is based on integrally closed Krasner hyperrings and (almost) integral dependence applications in krasner hyperrings.

___

  • Ameri, R. (2003) “On Categories of hypergroups and hypermodules”, Journal of Discrete Mathematical Sciences, 6:2-3, 121-132.
  • Bordbar, H. and Cristea, I. (2017) “Height of Prime Hyperideals in Krasner Hyperrings”, Filomat, 31:19,6153-6163.
  • Corsini, P. (1993) “Prolegomena of Hypergroup Theory”, 2nd ed. Tricesimo Italy, Aviani editore Italy.
  • Davvaz, B. and Fotea, V.L. (2007) “Hyperring Theory and Applications”, Palm Harbor, FL, USA, International Academic Press.
  • Davvaz, B. and Salasi, A. (2006) “A realization of hyperrings”, Comm. Algebra, 34, 4389-4400.
  • Krasner, M. (1999) “A class of hyperring and hyperfields”, IJMMS, 6:2,307-311.
  • Larsen, M.D. and McCarthy, P.J. (1971). “Multiplicative Theory of Ideals”, Pure and Applied athematics, A Series of Monographs and Textbooks,Volume 43, Academic Press, New York and London.
  • Mahjoob, R. and Ghaffari, V. (2018), “Zariski topology for second subhypermodules”, Italian Journal of Pure and Applied Mathematics, 39, 554-568.