2007/01/04 by Huishi Li, Li, Huishi
Mathematics · #16W70 #16Z05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.math/0701120
openalex publication_date 2007/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be an infinite field and K< X> =K< X1,...,Xn> the free associative algebra generated by X=\X1,...,Xn\ over K. It is proved that if I is a two-sided ideal of K< X> such that the K-algebra A=K< X> /I is almost commutative in the sense of [3], namely, with respect to its standard ℕ-filtration FA, the associated ℕ-graded algebra G(A) is commutative, then I is generated by a finite Gröbner basis. Therefor, every quotient algebra of the enveloping algebra U(g) of a finite dimensional K-Lie algebra g is, as a noncommutative algebra of the form A=K< X> /I, defined by a finite Gröbner basis in K< X>.