可解多项式代数与它在阶滤子下两种分次代数的关系

Relationship between solvable polynomial algebra and its two kinds of graded algebra under order filtration

针对可解多项式代数A,证明了它在阶滤子下两种分次代数grC(A)与 A均为可解多项式代数.应用Groeb ner基理论,给出了其左理想L和grC(L)与 L的Groebner基的转换.

It is proved that, when A is a solvable polynomial algebra, its two kinds of graded algebra are also solvable polyonmial algebra. Using Groebner basis theory, the transfer from Groebner basis of its left ideal to that of its two kinds of graded algebra grC(L) and   under the order filtration is given.