A Theorem on Finite Generation of a Ring
A Theorem on Finite Generation of a Ring
复制标题
环的有限生成定理
DOI：
10.1017/s0027763000011995
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发表时间：
1966
影响因子：
0.8
通讯作者：
M. Nagata
中科院分区：
文献类型：
--
作者：
M. Nagata
希尔伯特的第十四个问题要求某一类环的有限生成，并有一个反例(参看。[4]))。另一方面，许多数学家给出了这类环有限生成的各种充分条件(见[9]、[5]和[8])。本文的目的是给出一个新的充分条件。要处理的环的类别比以前处理的环的类别要普遍得多，除了[8]中的那一个。
The fourteenth problem of Hilbert asked finite generation of a certain class of rings and had a counter-example (cf. [4]). On the other hand, many mathematicians gave various sufficient conditions for finite generation of such rings (see, for instance, [9], [5] and [8]). The purpose of the present paper is to give a new sufficient condition. The class of rings to be treated is much more general than those treated before, except for the one in [8].