An elimination lemma for algebras with PBW bases

作者：Li, Huishi^*

来源：Communications in Algebra, 2018, 46(8): 3520-3532.

DOI：10.1080/00927872.2018.1424863

• Elimination
• filtration
• Gelfand-Kirillov dimension
• Grobner basis
• PBW basis

Let K be a field, and a finitely generated K-algebra with the PBW K-basis. It is shown that if L is a nonzero left ideal of A with GK.dim(A/L)=d<n (= the number of generators of A), then L has the elimination property in the sense that V(U)L{0} for every subset with In terms of the structural properties of A, it is also explored when the condition GK.dim(A/L)<n may hold for a left ideal L of A. Moreover, from the viewpoint of realizing the elimination property by means of Grobner bases, it is demonstrated that if A is in the class of binomial skew polynomial rings or in the class of solvable polynomial algebras, then every nonzero left ideal L of A satisfies GK.dim(A/L)< GK.dimA=n (= the number of generators of A), thereby L has the elimination property.

• 单位
  海南大学