论文标题
在semigroup $ \ boldsymbol {b}_Ω^{\ mathscr {f} _n} $的射型内态的半群上，该'
On the semigroup of injective endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}_n}$ which is generated by the family $\mathscr{F}_n$ of initial finite intervals of $ω$
论文作者
论文摘要
在本文中，我们描述了反向半群的射态内态性$ \ boldsymbol {b}_Ω^{\ mathscr {f}} $，该{f}} $，在论文[O. Gutik和M. Mykhalenych，\ emph {关于Bicyclic Monoid的某些概括}，Visnyk lviv。大学。 ser。 Mech.-Mat。 \ textbf {90}（2020），5--19（在乌克兰人）]，如果家族$ \ mathscr {f} _n $是由集合$ \ {0,1，\ ldots，n \} $生成的。特别是我们表明，半群$ \ boldsymbol {b}_Ω^{\ mathscr {f}} $的射入性内态的半群是同构对$（ω，+）$。另外，我们还描述了$λ{\ times}λ$ -MATRIX UNITS $ \ MATHSCR $ \ MATHSCR {B}_λ$ $。
In the paper we describe injective endomorphisms of the inverse semigroup $\boldsymbol{B}_ω^{\mathscr{F}}$, which is introduced in the paper [O. Gutik and M. Mykhalenych, \emph{On some generalization of the bicyclic monoid}, Visnyk Lviv. Univ. Ser. Mech.-Mat. \textbf{90} (2020), 5--19 (in Ukrainian)], in the case when the family $\mathscr{F}_n$ is generated by the set $\{0,1,\ldots,n\}$. In particular we show that the semigroup of injective endomorphisms of the semigroup $\boldsymbol{B}_ω^{\mathscr{F}}$ is isomorphic to $(ω,+)$. Also we describe the structure of the semigroup $\mathfrak{End}(\mathscr{B}_λ)$ of all endomorphisms of the semigroup of $λ{\times}λ$-matrix units $\mathscr{B}_λ$.
