Derivations on the matrix semirings of max-plus algebra
Let $(S,\oplus,\otimes)$ be a matrix semiring of max-plus algebra with the addition operation $\oplus$ and the multiplication operation $\otimes$, where the set \( S \) consists of matrices constructed from real numbers together with the element negative infinity. A derivation on the semiring \(S\)...
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Shahid Bahonar University of Kerman
2024-12-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4623_d3b3ad2c969dce5b0080c60c5deea3bc.pdf |
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| author | Suffi Nuralesa Nikken Puspita |
| author_facet | Suffi Nuralesa Nikken Puspita |
| author_sort | Suffi Nuralesa |
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| description | Let $(S,\oplus,\otimes)$ be a matrix semiring of max-plus algebra with the addition operation $\oplus$ and the multiplication operation $\otimes$, where the set \( S \) consists of matrices constructed from real numbers together with the element negative infinity. A derivation on the semiring \(S\) is an additive mapping \(\delta\) from \(S\) to itself that satisfies the axiom \(\delta(x \otimes y) = (\delta(x) \otimes y) \oplus (x \otimes \delta(y))\), for every \(x, y \in S\). From $S$ we construct all of semiring derivations of $S$ are denoted by $D$. On the set $D$, we defined two binary operations, i.e., addition "$\dotplus$" and composition "$\circ$". We want to investigate the structure of $D$ over "$\dotplus$" and "$\circ$" operations. We show that \( D \) is not a semiring, but there exists a sub-semiring \( H \) \(\subseteq\) \( D \). Here, triple $(H,\oplus,\circ)$ is a semiring which is constructed from max-plus algebra. |
| format | Article |
| id | doaj-art-1745d0dac7f943bdadffa6245aa1fb75 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-1745d0dac7f943bdadffa6245aa1fb752025-01-04T19:29:56ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052024-12-01135516310.22103/jmmr.2024.23345.16354623Derivations on the matrix semirings of max-plus algebraSuffi Nuralesa0Nikken Puspita1Department of Mathematics, Universitas Diponegoro, Semarang, IndonesiaDepartment of Mathematics, Universitas Diponegoro, Semarang, IndonesiaLet $(S,\oplus,\otimes)$ be a matrix semiring of max-plus algebra with the addition operation $\oplus$ and the multiplication operation $\otimes$, where the set \( S \) consists of matrices constructed from real numbers together with the element negative infinity. A derivation on the semiring \(S\) is an additive mapping \(\delta\) from \(S\) to itself that satisfies the axiom \(\delta(x \otimes y) = (\delta(x) \otimes y) \oplus (x \otimes \delta(y))\), for every \(x, y \in S\). From $S$ we construct all of semiring derivations of $S$ are denoted by $D$. On the set $D$, we defined two binary operations, i.e., addition "$\dotplus$" and composition "$\circ$". We want to investigate the structure of $D$ over "$\dotplus$" and "$\circ$" operations. We show that \( D \) is not a semiring, but there exists a sub-semiring \( H \) \(\subseteq\) \( D \). Here, triple $(H,\oplus,\circ)$ is a semiring which is constructed from max-plus algebra.https://jmmrc.uk.ac.ir/article_4623_d3b3ad2c969dce5b0080c60c5deea3bc.pdfsemiringsmatrix semiringderivationmax-plus algebra |
| spellingShingle | Suffi Nuralesa Nikken Puspita Derivations on the matrix semirings of max-plus algebra Journal of Mahani Mathematical Research semirings matrix semiring derivation max-plus algebra |
| title | Derivations on the matrix semirings of max-plus algebra |
| title_full | Derivations on the matrix semirings of max-plus algebra |
| title_fullStr | Derivations on the matrix semirings of max-plus algebra |
| title_full_unstemmed | Derivations on the matrix semirings of max-plus algebra |
| title_short | Derivations on the matrix semirings of max-plus algebra |
| title_sort | derivations on the matrix semirings of max plus algebra |
| topic | semirings matrix semiring derivation max-plus algebra |
| url | https://jmmrc.uk.ac.ir/article_4623_d3b3ad2c969dce5b0080c60c5deea3bc.pdf |
| work_keys_str_mv | AT suffinuralesa derivationsonthematrixsemiringsofmaxplusalgebra AT nikkenpuspita derivationsonthematrixsemiringsofmaxplusalgebra |