2014/01/20 by Huishi Li, Li, Huishi
Mathematics · #16W70 #16Z05 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Secondary 16W70 #math.RA #msc:16W70 #msc:16Z05
paper · pdf · doi:10.48550/arxiv.1401.4836
13 pages. Algorithm1, Algorithm 2, and Algorithm 3 are revised
openalex publication_date 2014/01/20 · arxiv created 2015/06/19 · arxiv updated 2015/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \KX =K⟨ X1,… ,Xn⟩ be the free algebra generated by X=\ X1,… ,Xn\ over a field K. It is shown that with respect to any weighted ℕ-gradation attached to \KX, minimal homogeneous generating sets for finitely generated graded (two-sided) ideals of \KX can be algorithmically computed, and that if an ungraded (two-sided) ideal I of \KX has a finite Gröbner basis \G with respect to a graded monomial ordering on \KX, then a minimal standard basis for I can be computed via computing a minimal homogeneous generating set of the associated graded ideal ⟨\LH (I)⟩.