University of KashanMathematics Interdisciplinary Research2538-36396420211201Hyperideals of (Finite) General Hyperrings25727311163710.22052/mir.2021.240436.1269ENReza AmeriSchool of Mathematics,
Statistic and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran0000-0001-5760-1788Mohammad HamidiDepartment of Mathematics,
Payame Noor University,
Tehran, I. R. IranHoda MohammadiDepartment of Mathematics,
Payame Noor University,
Tehran, I. R. IranJournal Article20210119A 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