论文标题
在$ \ mathbb {n} $的cofinite部分异构体上，带有通常的度量
On the monoid of cofinite partial isometries of $\mathbb{N}$ with the usual metric
论文作者
论文摘要
In the paper we show that the monoid $\mathbf{I}\mathbb{N}_{\infty}$ of all partial cofinite isometries of positive integers does not embed isomorphically into the monoid $\mathbf{ID}_{\infty}$ of all partial cofinite isometries of integers.此外，每个非宣传同构$ \ mathfrak {h} \ colon \ colon \ mathbf {i} $（\ mathbf {i} \ Mathbb {n} _ {\ infty}）\ Mathfrak {h} $是两元素环组$ \ mathbb {z} _2 $或对整数$ \ mathbb {z} $添加的添加剂组。另外，我们证明了MONOID $ \ MATHBF {I} \ MATHBB {n} _ {\ infty} $不是有限生成的，此外，Monoid $ \ Mathbf {i} \ Mathbb {i} \ Mathbb {n} _ {n} _ {\ infty} $不包含Minimal Generation Setate。
In the paper we show that the monoid $\mathbf{I}\mathbb{N}_{\infty}$ of all partial cofinite isometries of positive integers does not embed isomorphically into the monoid $\mathbf{ID}_{\infty}$ of all partial cofinite isometries of integers. Moreover, every non-annihilating homomorphism $\mathfrak{h}\colon \mathbf{I}\mathbb{N}_{\infty}\to\mathbf{ID}_{\infty}$ has the following property: the image $(\mathbf{I}\mathbb{N}_{\infty})\mathfrak{h}$ is isomorphic either to the two-element cyclic group $\mathbb{Z}_2$ or to the additive group of integers $\mathbb{Z}(+)$. Also we prove that the monoid $\mathbf{I}\mathbb{N}_{\infty}$ is not finitely generated, and, moreover, monoid $\mathbf{I}\mathbb{N}_{\infty}$ does not contain a minimal generating set.
