On injective endomorphisms of the semigroup $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$
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| Format: | Preprint |
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2025
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| _version_ | 1866908731560689664 |
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| author | Gutik, Oleg Pozdniakova, Inna |
| author_facet | Gutik, Oleg Pozdniakova, Inna |
| contents | We describe injective endomorphisms of the semigroup $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$. In particular we show that every injective endomorphism $\mathfrak{e}$ of $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ is presented in the form $\mathfrak{e}=\mathfrak{e}_0\mathfrak{a}$, where $\mathfrak{e}_0$ is an injective $(0,0,[0))$-endomorphism of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ and $\mathfrak{a}$ is an automorphism $\mathfrak{a}$ of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$. Also we describe all injective $(0,0,[0))$-endomorphisms $\mathfrak{e}_0$ of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$, i.e., such that $(0,0,[0))\mathfrak{e}_0=(0,0,[0))$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_21387 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On injective endomorphisms of the semigroup $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$ Gutik, Oleg Pozdniakova, Inna Group Theory 20M18, 20F29, 20M10 We describe injective endomorphisms of the semigroup $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$. In particular we show that every injective endomorphism $\mathfrak{e}$ of $\boldsymbol{B}_{Z\mathbb{}}^{\mathscr{F}^2}$ is presented in the form $\mathfrak{e}=\mathfrak{e}_0\mathfrak{a}$, where $\mathfrak{e}_0$ is an injective $(0,0,[0))$-endomorphism of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ and $\mathfrak{a}$ is an automorphism $\mathfrak{a}$ of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$. Also we describe all injective $(0,0,[0))$-endomorphisms $\mathfrak{e}_0$ of $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$, i.e., such that $(0,0,[0))\mathfrak{e}_0=(0,0,[0))$. |
| title | On injective endomorphisms of the semigroup $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$ |
| topic | Group Theory 20M18, 20F29, 20M10 |
| url | https://arxiv.org/abs/2508.21387 |