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Derivations on the matrix semirings of max-plus algebra | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 5 - شماره پیاپی 30، اسفند 2024، صفحه 51-63 اصل مقاله (462.76 K) | ||
| نوع مقاله: Special Issue: First Joint IIIMT-Algebra Forum Conference 2023 | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23345.1635 | ||
| نویسندگان | ||
| Suffi Nuralesa* ؛ Nikken Prima Puspita | ||
| Department of Mathematics, Universitas Diponegoro, Semarang, Indonesia | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Semirings؛ Matrix Semiring؛ Derivation؛ Max-plus Algebra | ||
| مراجع | ||
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