The maximal hyperrings of quotients


Durna H. , Yılmaz D., Davvaz B.

Italian Journal of Pure and Applied Mathematics, vol.44, no.2, pp.938-951, 2020 (Journal Indexed in ESCI)

  • Publication Type: Article / Article
  • Volume: 44 Issue: 2
  • Publication Date: 2020
  • Title of Journal : Italian Journal of Pure and Applied Mathematics
  • Page Numbers: pp.938-951

Abstract

We show that the maximal quotient hyperring Qmr(R) of a semiprime hyperring R can be obtained in a similar way to a maximal quotient ring. In this regard we introduce and study some basic notions of hyperrings such as dense hyperideal, essential hyperideal, singular hyperideal and prove some results satisfying them. Finally, we show that if R is a semiprime hyperring and Q = Qmr(R), then Q is regular (in the sense of von Neumann) if and only if R has a zero right singular hyperideal.