arXiv subjects

Marko Serivka

Publications and source records attributed to Marko Serivka.

4 recordsLinked to original sources

arXiv2026

On injective endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^4}$ with a four-element family $\mathscr{F}^4$ of inductive non-empty subsets of $\omega$

We describe injective endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^4}$ with a four-element family $\mathscr{F}^4$ of inductive non-empty subsets of $\omega$. In particular we proved that every injective monoid endomorphism of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^4}$ is the identity transformation. Also we describe all (not necessary monoid) injective endomorphism of $\boldsymbol{B}_{\omega}^{\mathscr{F}^4}$.

math.GR↗

arXiv2025

On injective endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^3}$ with a three-element family $\mathscr{F}^3$ of inductive non-empty subsets of $\omega$

We describe injective endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^3}$ with a three-element family $\mathscr{F}^3$ of inductive non-empty subsets of $\omega$. In particular we find endomorphisms $\varpi_3$ and $\lambda$ of $\boldsymbol{B}_{\omega}^{\mathscr{F}^3}$ such that for every injective endomorphism $\varepsilon$ of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^3}$ there exists an injective endomorphism $\iota\in\left\langle\lambda,\varpi_3\right\rangle$ such that $\varepsilon=\alpha_{[k]}\circ\iota$ for some positive integer $k$, where $\alpha_{[k]}$ is an injective monoid endomorphism of $\boldsymbol{B}_{\omega}^{\mathscr{F}^3}$.

math.GR↗

arXiv2025

On the semigroup of endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $\omega$

We study the semigroup $\overline{\boldsymbol{End}}(\boldsymbol{B}_{\omega}^{\mathscr{F}^2})$ of all endomorphisms of the bicyclic extension $\boldsymbol{B}_{\omega}^{\mathscr{F}^2}$ with the two-element family $\mathscr{F}^2$ of inductive nonempty subsets of $\omega$. The submonoid $\left\langle\varpi\right\rangle^1$ of $\overline{\boldsymbol{End}}(\boldsymbol{B}_{\omega}^{\mathscr{F}^2})$ with the property that every element of the semigroup $\overline{\boldsymbol{End}}(\boldsymbol{B}_{\omega}^{\mathscr{F}^2})$ has the unique representation as the product of the monoid endomorphism of $\boldsymbol{B}_{\omega}^{\mathscr{F}^2}$ and the element of $\left\langle\varpi\right\rangle^1$ is constructed.

math.GR↗

arXiv2024

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 $ω$

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.

math.GR↗