可解多项式代数上的泛左Gröbner基

Universal Left Gröbner Bases on Solvable Polynomial Algebra

设I是可解多项式代数A=K[a_1,…,a_n]的一个非零左理想,由可解多项式代数上的左Grbner基性质,可知A中任何一个左理想对于一个单项式序的左Grbner基不一定满足另一个单项式序.首先证明了在B上的任意2个单项式序<1,<2下,g={g1,g2,…,gt}是I在<1下的左Grbner基,若LM<1(gi)=LM<2(gi),1≤i≤t,那么g={g1,g2,…,gt}也是I在<2下的左Grbner基;其次证明了I在A上的所有单项式序(可能无限个)下只有有限个约化左Grbner基;最后证明了A中的一个子集F,对于其上的任何一个单项式序,都是I的左Grbner基,子集F就是A的泛左Grbner基.

In the report,let I be a nonzero left ideal of a solvable polynomial algebra A = K[a1,…,an],based on the property of left Grobher of the solvable polynonlial algebra,we know that a len Grobner bases with respect to one monomial ordering might not be a left Grobner bases with respect to another monomial ordering. First,it was proved that〈 1,〈2,B,g = { g1,g2,…,gt},is the left Grobher bases of I with respect to 〈1,if LM〈1（ gi） =LM〈2（ gi）,1≤i≤t,then g = { g1,g2,…,gt} is also the left Grobher bases of I with respect to 〈2; Second,it was proved that there are only finitely many possible reduced left Grobner bases for a given left ideal; Last,a subset of A,f,is a left Grobner bases with respect to every ordering,and which is called a universal left Grobner bases of A.