论文标题
权力群体的半度和互动身份
Semiring and involution identities of power groups
论文作者
论文摘要
对于每个组$ g $，其子集的集合$ \ MATHCAL {p}（g）$构成集合理论结合$ \ cup $和元素乘法$ \ cdot $ sem semiring semir，并形成了$ \ cdot $和元素wise-wise-wise wise invernion $ {}^}^{ - 1} $。 We show that if the group $G$ is finite, non-Dedekind, and solvable, neither the semiring $(\mathcal{P}(G),\cup,\cdot)$ nor the involution semigroup $(\mathcal{P}(G),\cdot,{}^{-1})$ admits a finite identity basis.我们还解决了在任何有限套装上半厅关系的有限基础问题。
For every group $G$, the set $\mathcal{P}(G)$ of its subsets forms a semiring under set-theoretical union $\cup$ and element-wise multiplication $\cdot$ and forms an involution semigroup under $\cdot$ and element-wise inversion ${}^{-1}$. We show that if the group $G$ is finite, non-Dedekind, and solvable, neither the semiring $(\mathcal{P}(G),\cup,\cdot)$ nor the involution semigroup $(\mathcal{P}(G),\cdot,{}^{-1})$ admits a finite identity basis. We also solve the finite basis problem for the semiring of Hall relations over any finite set.
