Realization of monoids with countable sum
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917675757731840 |
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| author | Nazemian, Zahra |
| author_facet | Nazemian, Zahra |
| contents | For every infinite cardinal number $κ$, $κ$-monoids and their realization have recently been introduced and studied by Nazemian and Smertnig. A $κ$-monoid $H$ has a realization to a ring $R$ if there exists an element $x \in H$ such that $H$ is $\aleph_1 ^{-}$-braided over $\text{add}(\aleph_0 x)$, and $\text{add}(\aleph_0 x)$, as $\aleph_0$-monoid, has a realization to $R$. Furthermore, $H$ has a realization to hereditary rings if there exists an element $x \in H$ such that $H$ is braided over $\text{add}(x)$. These prompt an investigation into when $\aleph_0$-monoids have realizations. In this paper, we discuss the realization of $\aleph_0$-monoids and provide a complete characterization for the realization of two-generated ones in hereditary Von Neumann regular rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Realization of monoids with countable sum Nazemian, Zahra Representation Theory Primary 16D70, Secondary 16D40, 16E50, 16P10, 16S99 For every infinite cardinal number $κ$, $κ$-monoids and their realization have recently been introduced and studied by Nazemian and Smertnig. A $κ$-monoid $H$ has a realization to a ring $R$ if there exists an element $x \in H$ such that $H$ is $\aleph_1 ^{-}$-braided over $\text{add}(\aleph_0 x)$, and $\text{add}(\aleph_0 x)$, as $\aleph_0$-monoid, has a realization to $R$. Furthermore, $H$ has a realization to hereditary rings if there exists an element $x \in H$ such that $H$ is braided over $\text{add}(x)$. These prompt an investigation into when $\aleph_0$-monoids have realizations. In this paper, we discuss the realization of $\aleph_0$-monoids and provide a complete characterization for the realization of two-generated ones in hereditary Von Neumann regular rings. |
| title | Realization of monoids with countable sum |
| topic | Representation Theory Primary 16D70, Secondary 16D40, 16E50, 16P10, 16S99 |
| url | https://arxiv.org/abs/2404.15769 |