Recognizing the Semiprimitivity of N-graded Algebras via Grobner Bases

• 作者: Huishi Li
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: K-代数 Grobner基 单项式序 非齐次 S代数 REE 半素 理想
• 年，卷（期）: 2015,（3）
• 页码范围: 459-468
• 页数: 10页
• 分类号: O154.3
• 语种: 中文

摘要

Let K〈X〉 = K(X1,..., Xn) be the free K-algebra on X = {X1,..., Xn} over a field K, which is equipped with a weight N-gradation (i.e., each Xi is assigned a positive degree), and let G be a finite homogeneous GrSbner basis for the ideal I = (G) of K(X) with respect to some monomial ordering 〈 on K(X). It is shown that if the monomial algebra K(X)/(LM(6)) is semiprime, where LM(6) is the set of leading monomials of 6 with respect to 〈, then the N-graded algebra A : K(X)/I is semiprimitive in the sense of Jacobson. In the case that G is a finite nonhomogeneous Gr6bner basis with respect to a graded monomial ordering 〈gr, and the N-filtration FA of the algebra A = K(X)/I induced by the N-grading filtration FK(X) of K(X) is considered, if the monomial algebra K(X)/(LM(6)) is semiprime, then it is shown that the associated N-graded algebra G(A) and the Rees algebra A of A determined by FA are all semiprimitive.