论文标题
在分裂代数中存在非平凡的$ s_n $ invariants的必要条件
A necessary and sufficient condition for the existence of non-trivial $S_n$-invariants in the splitting algebra
论文作者
论文摘要
对于交换性的一元多项式$ f $，统一戒指$ a $ a $ spripting代数$ a_f $是通用$ a $ a $ algebra，因此$ f $ a_f $ a_f $。对称组通过将$ f $的根部定为拆分代数。众所周知，如果元素$ 2 $和$ d_f $（其中$ d_f $取决于$ f $）的nihihilators的交汇处为$ a $零，则在集体操作下的不变性剂完全等于$ a $。我们证明了相反的人。
For a monic polynomial $f$ over a commutative, unitary ring $A$ the splitting algebra $A_f$ is the universal $A$-algebra such that $f$ splits in $A_f$. The symmetric group acts on the splitting algebra by permuting the roots of $f$. It is known that if the intersection of the annihilators of the elements $2$ and $D_f$ (where $D_f$ depends on $f$) in $A$ is zero, then the invariants under the group action are exactly equal to $A$. We show that the converse holds.
