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 \(S\)...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2024-12-01
|
| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4623_d3b3ad2c969dce5b0080c60c5deea3bc.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2251-7952 2645-4505 |