On the semigroup of endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^2}$ 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_ | 1866909927514046464 |
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| author | Gutik, Oleg Serivka, Marko |
| author_facet | Gutik, Oleg Serivka, Marko |
| contents | We study the semigroup $\overline{\boldsymbol{End}}(\boldsymbol{B}_ω^{\mathscr{F}^2})$ of all endomorphisms of the bicyclic extension $\boldsymbol{B}_ω^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$. The submonoid $\left\langle\varpi\right\rangle^1$ of $\overline{\boldsymbol{End}}(\boldsymbol{B}_ω^{\mathscr{F}^2})$ with the property that every element of the semigroup $\overline{\boldsymbol{End}}(\boldsymbol{B}_ω^{\mathscr{F}^2})$ has the unique representation as the product of the monoid endomorphism of $\boldsymbol{B}_ω^{\mathscr{F}^2}$ and the element of $\left\langle\varpi\right\rangle^1$ is constructed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_18837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the semigroup of endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$ Gutik, Oleg Serivka, Marko Group Theory 20M10, 20M15, 20M18 We study the semigroup $\overline{\boldsymbol{End}}(\boldsymbol{B}_ω^{\mathscr{F}^2})$ of all endomorphisms of the bicyclic extension $\boldsymbol{B}_ω^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$. The submonoid $\left\langle\varpi\right\rangle^1$ of $\overline{\boldsymbol{End}}(\boldsymbol{B}_ω^{\mathscr{F}^2})$ with the property that every element of the semigroup $\overline{\boldsymbol{End}}(\boldsymbol{B}_ω^{\mathscr{F}^2})$ has the unique representation as the product of the monoid endomorphism of $\boldsymbol{B}_ω^{\mathscr{F}^2}$ and the element of $\left\langle\varpi\right\rangle^1$ is constructed. |
| title | On the semigroup of endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $ω$ |
| topic | Group Theory 20M10, 20M15, 20M18 |
| url | https://arxiv.org/abs/2506.18837 |