Hyperideals of (Finite) General Hyperrings
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 r...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Kashan
2021-12-01
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| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_111637_7393b508a7b45a38ca94f4530cfee81c.pdf |
| _version_ | 1797630856955691008 |
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| author | Reza Ameri Mohammad Hamidi Hoda Mohammadi |
| author_facet | Reza Ameri Mohammad Hamidi Hoda Mohammadi |
| author_sort | Reza Ameri |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T11:13:52Z |
| format | Article |
| id | doaj.art-d759f680282c4022a7d23c9684b61795 |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:52Z |
| publishDate | 2021-12-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-d759f680282c4022a7d23c9684b617952023-11-11T10:03:29ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652021-12-016425727310.22052/mir.2021.240436.1269111637Hyperideals of (Finite) General HyperringsReza Ameri0Mohammad Hamidi1Hoda Mohammadi2School of Mathematics, Statistic and Computer Sciences, University of Tehran, Tehran, I. R. IranDepartment of Mathematics, Payame Noor University, Tehran, I. R. IranDepartment of Mathematics, Payame Noor University, Tehran, I. R. IranA 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.pdfgeneral hyperringhyperidealskrasner hyperring |
| spellingShingle | Reza Ameri Mohammad Hamidi Hoda Mohammadi Hyperideals of (Finite) General Hyperrings Mathematics Interdisciplinary Research general hyperring hyperideals krasner hyperring |
| title | Hyperideals of (Finite) General Hyperrings |
| title_full | Hyperideals of (Finite) General Hyperrings |
| title_fullStr | Hyperideals of (Finite) General Hyperrings |
| title_full_unstemmed | Hyperideals of (Finite) General Hyperrings |
| title_short | Hyperideals of (Finite) General Hyperrings |
| title_sort | hyperideals of finite general hyperrings |
| topic | general hyperring hyperideals krasner hyperring |
| url | https://mir.kashanu.ac.ir/article_111637_7393b508a7b45a38ca94f4530cfee81c.pdf |
| work_keys_str_mv | AT rezaameri hyperidealsoffinitegeneralhyperrings AT mohammadhamidi hyperidealsoffinitegeneralhyperrings AT hodamohammadi hyperidealsoffinitegeneralhyperrings |