论文标题
正式电力系列半群的正确舒适性
Right amenability in semigroups of formal power series
论文作者
论文摘要
让$ k $是特征零的代数封闭场，而$ k [[z]] $超过$ k $的正式电源圈。我们提供了几种$ z^2k [[z]] $有限生成的右生成的子元素的特征，而semigroup操作$ \ circ $是构图。特别是，我们表明一个子元素$ s = \ langle q_1，q_2，\ dots，q_k \ rangle $的$ z^2k [[z]] $是正确的，并且仅当存在可逆元素$β$β$ q kk [z] $ civie $β^cive = cive^cive^cive = - z^{d_i}，$ 1 \ leq i \ leq k，$ for某些整数$ d_i $，$ 1 \ leq i \ leq k，$ and $ and unity $ω_i，$ 1 \ $ 1 \ leq i \ leq i \ leq i \ leqk。$ $
Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$ the ring of formal power series over $k$. We provide several characterizations of right amenable finitely generated subsemigroups of $z^2k[[z]]$ with the semigroup operation $\circ $ being composition. In particular, we show that a subsemigroup $S=\langle Q_1,Q_2,\dots, Q_k\rangle$ of $z^2k[[z]]$ is right amenable if and only if there exists an invertible element $β$ of $zk[[z]]$ such that $β^{-1}\circ Q_i \circ β=ω_i z^{d_i},$ $1\leq i \leq k,$ for some integers $d_i$, $1\leq i \leq k,$ and roots of unity $ω_i,$ $1\leq i \leq k.$
