On finite generation of Noetherian algebras over two-dimensional regular local rings
On finite generation of Noetherian algebras over two-dimensional regular local rings
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二维正则局部环上诺特代数的有限生成
DOI：
10.1016/j.jalgebra.2020.05.013
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发表时间：
2020
影响因子：
0.9
通讯作者：
Onoda Nobuharu
中科院分区：
文献类型：
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作者：
Dutta Amartya Kumar;Gupta Neena;Onoda Nobuharu
设R是具有代数闭剩余域的完备正则局部环，A是多项式环R [X]的Noether R-子代数.在[4]中已经证明，如果dim R= 1，则A必然是R上的n-生成的。本文给出了当dim R= 2时，A在R上生成的充要条件，并给出了R= C [[u，v]]上R [X]的Noether正规非生成R-子代数的一个例子.
Let R be a complete regular local ring with an algebraically closed residue field and let A be a Noetherian R-subalgebra of the polynomial ring R [X]. It has been shown in [4] that if dim R= 1, then A is necessarily finitely generated over R. In this paper, we give necessary and sufficient conditions for A to be finitely generated over R when dim R= 2 and present an example of a Noetherian normal non-finitely generated R-subalgebra of R [X] over R= C [[u, v]].