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整环的赋值扩环及赋值维数

, PP. 419-425

Keywords: 整环,赋值扩环,赋值维数

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Abstract:

设R是整环,其商域为K.dimv(R)表示R的赋值维数.证明了(1)dimv(R)是R的维数互异的既是UMT整环,又是DW整环的扩环升链RmRm-1…R1R0=K的长度的上确界;(2)dimv(R/P)≤dimv(R)-htvP,其中P是R的素理想,htvP是P的赋值高度;(3)对于强Milnor方图RDTF,dimv(R)=max{htvM+dimv(D),dimv(T)},其中M是R与T的公共素理想.

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