TY - JOUR
ID - 111637
TI - Hyperideals of (Finite) General Hyperrings
JO - Mathematics Interdisciplinary Research
JA - MIR
LA - en
SN - 2538-3639
AU - Ameri, Reza
AU - Hamidi, Mohammad
AU - Mohammadi, Hoda
AD - School of Mathematics,
Statistic and Computer Sciences,
University of Tehran,
Tehran, I. R. Iran
AD - Department of Mathematics,
Payame Noor University,
Tehran, I. R. Iran
Y1 - 2021
PY - 2021
VL - 6
IS - 4
SP - 257
EP - 273
KW - General hyperring
KW - Hyperideals
KW - Krasner hyperring
DO - 10.22052/mir.2021.240436.1269
N2 - 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.
UR - https://mir.kashanu.ac.ir/article_111637.html
L1 - https://mir.kashanu.ac.ir/article_111637_7393b508a7b45a38ca94f4530cfee81c.pdf
ER -