论文标题
代数换向器相对于分区环中的亚正态群
Algebraic commutators with respect to subnormal subgroups in division rings
论文作者
论文摘要
让$ d $是$ d $的一个分区环，$ k $，不一定包含在$ d $的中心$ f $中。在本文中，我们研究了$ d $ $ d $ $ d $ y $ k $的左代数条件下的$ d $的结构。在结果中，可以证明，如果$ d^*$包含一个非中央正常子组，该子组在有限度$ d $的$ k $上留下代数，则$ [d：f] \ le d^2 $。如果$ k = f $，获得的结果表明，如果所有添加剂换向器或所有乘法换向器相对于$ d^*$的非中央亚正常亚组是$ f $ abo $ f $ abo $ d $的代数，则是$ [d：f] \ le d^2 $。
Let $D$ be a division ring and $K$ a subfield of $D$ which is not necessarily contained in the center $F$ of $D$. In this paper, we study the structure of $D$ under the condition of left algebraicity of certain subsets of $D$ over $K$. Among results, it is proved that if $D^*$ contains a noncentral normal subgroup which is left algebraic over $K$ of bounded degree $d$, then $[D:F]\le d^2$. In case $K=F$, the obtained results show that if either all additive commutators or all multiplicative commutators with respect to a noncentral subnormal subgroup of $D^*$ are algebraic of bounded degree $d$ over $F$, then $[D:F]\le d^2$.
