F-rationality of the ring of modular invariants
F-rationality of the ring of modular invariants
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模不变量环的 F 理性
DOI：
10.1016/j.jalgebra.2017.04.017
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发表时间：
2017
影响因子：
0.9
通讯作者：
Mitsuyasu Hashimoto
中科院分区：
文献类型：
--
作者：
Mitsuyasu Hashimoto;Mitsuyasu Hashimoto;Mitsuyasu Hashimoto and Peter Symonds;Mitsuyasu Hashimoto
利用Symonds和作者对特征p>；0域上多项式环上有限群作用下不变量环上的模的Frobenius极限的刻画，给出了具有正对偶F-签名的不变量环的一个刻画.结合这一结果和Kemper关于置换群作用下不变量环深度的结果，我们给出了一个有限群作用下的F-有理但非F-正则不变量环的例子。
Using the description of the Frobenius limit of modules over the ring of invariants under an action of a finite group on a polynomial ring over a field of characteristic p> 0 developed by Symonds and the author, we give a characterization of the ring of invariants with a positive dual F-signature. Combining this result and Kemper's result on depths of the ring of invariants under an action of a permutation group, we give an example of an F-rational, but non-F-regular ring of invariants under the action of a finite group.