导代数DA_n的Krull维数与外乘积

Krull Dimension and External Product of Derivative Algebra DA _ n

证明了非零特征域上导代数ＤＡｎ 的Ｋｒｕｌｌ维数等于ｎ，并讨论了ＤＡｎ 模的外乘积，以及外乘积的滤子与分次结构、Ｇｅｌｆａｎｄ－Ｋｉｒｉｌｌｏｖ 维数和重数。

The Krull dimension of the derivative algebra DA n over a field of nonzero characteristic is proved to be n. The external product of DA n modules is defined. The filtration and graded structure, the Gelfand Kirillov dimensions and multiplicities of the external products of DA n modules are also investigated.