Hom-associative magmas with applications to Hom-associative magma algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910534364823552 |
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| author | Lundström, Patrik |
| author_facet | Lundström, Patrik |
| contents | Let $X$ be a magma, that is a set equipped with a binary operation, and consider a function $α: X \to X$. We that $X$ is Hom-associative if for all $x,y,z \in X$, the equality $α(x)(yz) = (xy) α(z)$ holds. For every isomorphism class of magmas of order two, we determine all functions $α$ making $X$ Hom-associative. Furthermore, we find all such $α$ that are endomorphisms of $X$. We also consider versions of these results where the binary operation on $X$ as well as the function $α$ may be only partially defined. We use our findings to construct examples of Hom-associative and multiplicative magma algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02341 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hom-associative magmas with applications to Hom-associative magma algebras Lundström, Patrik Rings and Algebras 08A05, 08A35, 17A01, 17D99, 20N02 Let $X$ be a magma, that is a set equipped with a binary operation, and consider a function $α: X \to X$. We that $X$ is Hom-associative if for all $x,y,z \in X$, the equality $α(x)(yz) = (xy) α(z)$ holds. For every isomorphism class of magmas of order two, we determine all functions $α$ making $X$ Hom-associative. Furthermore, we find all such $α$ that are endomorphisms of $X$. We also consider versions of these results where the binary operation on $X$ as well as the function $α$ may be only partially defined. We use our findings to construct examples of Hom-associative and multiplicative magma algebras. |
| title | Hom-associative magmas with applications to Hom-associative magma algebras |
| topic | Rings and Algebras 08A05, 08A35, 17A01, 17D99, 20N02 |
| url | https://arxiv.org/abs/2308.02341 |