On n-ary ring congruences of n-ary semirings
In universal algebra, it is well-known that if S is an algebraic structure, then the kind of algebraic structure of S/ρ is similar to S where ρ is a congruence relation on S. In this work, we study the notion of a full k-ideal A of an n-ary semiring S and construct a congruence relation ρ on S with...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20221019?viewType=HTML |
| _version_ | 1798036632881856512 |
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| author | Pakorn Palakawong na Ayutthaya Bundit Pibaljommee |
| author_facet | Pakorn Palakawong na Ayutthaya Bundit Pibaljommee |
| author_sort | Pakorn Palakawong na Ayutthaya |
| collection | DOAJ |
| description | In universal algebra, it is well-known that if S is an algebraic structure, then the kind of algebraic structure of S/ρ is similar to S where ρ is a congruence relation on S. In this work, we study the notion of a full k-ideal A of an n-ary semiring S and construct a congruence relation ρ on S with respect to the full k-ideal A in order to make the quotient n-ary semiring S/ρ to be an n-ary ring. Moreover, the notion of an h-ideal of an n-ary semiring was studied and connections between an h-ideal and a k-ideal of an n-ary semiring were investigated. |
| first_indexed | 2024-04-11T21:15:37Z |
| format | Article |
| id | doaj.art-285f790c42594421a5730b08be4619b0 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T21:15:37Z |
| publishDate | 2022-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-285f790c42594421a5730b08be4619b02022-12-22T04:02:49ZengAIMS PressAIMS Mathematics2473-69882022-08-01710185531856410.3934/math.20221019On n-ary ring congruences of n-ary semiringsPakorn Palakawong na Ayutthaya0Bundit Pibaljommee 1 Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandIn universal algebra, it is well-known that if S is an algebraic structure, then the kind of algebraic structure of S/ρ is similar to S where ρ is a congruence relation on S. In this work, we study the notion of a full k-ideal A of an n-ary semiring S and construct a congruence relation ρ on S with respect to the full k-ideal A in order to make the quotient n-ary semiring S/ρ to be an n-ary ring. Moreover, the notion of an h-ideal of an n-ary semiring was studied and connections between an h-ideal and a k-ideal of an n-ary semiring were investigated.https://www.aimspress.com/article/doi/10.3934/math.20221019?viewType=HTMLn-ary ringn-ary semiringring congruencek-idealh-ideal |
| spellingShingle | Pakorn Palakawong na Ayutthaya Bundit Pibaljommee On n-ary ring congruences of n-ary semirings AIMS Mathematics n-ary ring n-ary semiring ring congruence k-ideal h-ideal |
| title | On n-ary ring congruences of n-ary semirings |
| title_full | On n-ary ring congruences of n-ary semirings |
| title_fullStr | On n-ary ring congruences of n-ary semirings |
| title_full_unstemmed | On n-ary ring congruences of n-ary semirings |
| title_short | On n-ary ring congruences of n-ary semirings |
| title_sort | on n ary ring congruences of n ary semirings |
| topic | n-ary ring n-ary semiring ring congruence k-ideal h-ideal |
| url | https://www.aimspress.com/article/doi/10.3934/math.20221019?viewType=HTML |
| work_keys_str_mv | AT pakornpalakawongnaayutthaya onnaryringcongruencesofnarysemirings AT bunditpibaljommee onnaryringcongruencesofnarysemirings |