On the semigroup of injective monoid endomorphisms of the monoid $\boldsymbol{B}_ω^{\mathscr{F}^3}$ with a three element family $\mathscr{F}^3$ of inductive nonempty subsets of $ω$
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| Format: | Preprint |
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2024
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| _version_ | 1866929392938123264 |
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| author | Gutik, Oleg Serivka, Marko |
| author_facet | Gutik, Oleg Serivka, Marko |
| contents | We describe injective monoid endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^3}$ with a three element family $\mathscr{F}^3$ of inductive nonempty subsets of $ω$. Also, we show that the monoid $\boldsymbol{End}_*^1(\boldsymbol{B}_ω^{\mathscr{F}})$ of all injective endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^3}$ is isomorphic to the multiplicative semigroup of positive integers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_12414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the semigroup of injective monoid endomorphisms of the monoid $\boldsymbol{B}_ω^{\mathscr{F}^3}$ with a three element family $\mathscr{F}^3$ of inductive nonempty subsets of $ω$ Gutik, Oleg Serivka, Marko Group Theory 20M18, 20F29, 20M10 We describe injective monoid endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^3}$ with a three element family $\mathscr{F}^3$ of inductive nonempty subsets of $ω$. Also, we show that the monoid $\boldsymbol{End}_*^1(\boldsymbol{B}_ω^{\mathscr{F}})$ of all injective endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^3}$ is isomorphic to the multiplicative semigroup of positive integers. |
| title | On the semigroup of injective monoid endomorphisms of the monoid $\boldsymbol{B}_ω^{\mathscr{F}^3}$ with a three element family $\mathscr{F}^3$ of inductive nonempty subsets of $ω$ |
| topic | Group Theory 20M18, 20F29, 20M10 |
| url | https://arxiv.org/abs/2404.12414 |