非零特征域上导代数的GelfandKirillov维数理论

Gelfand Kirillov Dimension of Derivative Algebra for the Field of Nonzero Characteristic

给出了非零特征域上导代数ＤＡｎ 的ＧｅｌｆａｎｄＫｉｒｉｌｌｏｖ 维数的定义，并证明它等于ｎ ．然后，得到了任意有限生成左ＤＡｎ模的ＧＫ 维数只能为０ ，１ ，…，ｎ 中的某一个，且存在左ＤＡｎ模Ｍｉ，其ＧＫ 维数等于ｉ，其中ｉ 是０ ，１ ，…，ｎ

The definition of Gelfand Kirillov dimension of the derivative algebra on a field of nonzero characteristic is defined. The dimension is proven to be n . This result concludes that the G?K dimension of any finitely generated left DA n module can only be one of ｛0,1,…, n ｝, and there does exist a left DA n module M i whose G?K demension is i , where i is one of 0,1,…, n .