For a regular representation $H \subseteq \text{Sym}_n$ of the generalizedquaternion group of order $n=4k$, with $k\geq 2$, the monoid $S_n(H)$ presentedwith generators $a_1,a_2,\dots ,a_n$ and with relations $a_1a_2\cdotsa_n=a_{\sigma(1)}a_{\sigma(2)}\cdots a_{\sigma(n)}$, for all $\sigma\in H$, isinvestigated. It is shown that $S_n(H)$ has the two unique product property. Asa consequence, for any field $K$, the monoid algebra $K[S_n(H)]$ is a domainwith trivial units which is semiprimitive.
展开▼
机译：对于顺序为$ n = 4k $的广义四元数组的正则表示$ H \ subseteq \ text {Sym} _n $，其中$ k \ geq 2 $，则等式$ S_n（H）$与生成器$ a_1，a_2一起出现， \ dots，a_n $并与关系$ a_1a_2 \ cdotsa_n = a _ {\ sigma（1）} a _ {\ sigma（2）} \ cdots a _ {\ sigma（n）} $，适用于所有$ \ sigma \ in H $ ，正在调查中。显示$ S_n（H）$具有两个唯一的乘积属性。结果，对于任何字段$ K $，单面体代数$ K [S_n（H）] $是一个具有琐碎单位的域，它是半原始的。
展开▼
