Realization of monoids with countable sum
| Autor: | Nazemian, Zahra |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For every infinite cardinal number $\kappa$, $\kappa$-monoids and their realization have recently been introduced and studied by Nazemian and Smertnig. A $\kappa$-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. Comment: 25 Pages |
| Databáze: | arXiv |
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