University of Kashan Mathematics Interdisciplinary Research 2538-3639 6 4 2021 12 01 Hyperideals of (Finite) General Hyperrings 257 273 111637 10.22052/mir.2021.240436.1269 EN Reza Ameri School of Mathematics, Statistic and Computer Sciences, University of Tehran, Tehran, I. R. Iran 0000-0001-5760-1788 Mohammad Hamidi Department of Mathematics, Payame Noor University, Tehran, I. R. Iran Hoda Mohammadi Department of Mathematics, Payame Noor University, Tehran, I. R. Iran Journal Article 2021 01 19 A general hyperring is an algebraic hypercompositional system (R,+,·) with two hyperoperations ”+" and ” · ”, such that for all x,y ∈ R, x + y and x · y are non-empty subsets of R, and R satisfies the axioms similar to a ring. We introduce and study hyperideals of a general hyperring. In this regards, we construct a connection between classical rings and general hyperrings, specifically, we extend a ring to a general hyperring in nontrivial way. Moreover, a way to construct a general hyperring from set are given. Also, we concentrate on an important class of general hyperrings, which is called Krasner hyperrings, and discuss on their hyperideals. Finally, the set of all hyperideals of a finite general (resp. Krasner) hyperring are considered and its hyperideals are investigated. https://mir.kashanu.ac.ir/article_111637_7393b508a7b45a38ca94f4530cfee81c.pdf