1999/03/05 by Dmitri Piontkovsky, Piontkovsky, Dmitri
Mathematics · #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA #msc:16W50
paper · pdf · doi:10.48550/arxiv.math/9903030
17 pages in Latex2e, To appear in Proc. of Moscow-Tainan Algebraic Workshop
arxiv created 1999/03/05 · openalex publication_date 1999/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose A is a graded associative algebra over a field, I is its ideal generated by a set α of homogeneous elements, and B = A/I. In this note, some inequalities between Hilbert series of algebras A,B and the number of elements of the set α are announced. As in the Golod--Shafarevich inequality as in our case the equality in every estimate is exact iff the set α is strongly free: so we obtain some new characterizations of such sets. As a consequence it is proved that over a field of zero characteristic for the class of finitely defined graded algebras there is no algorithm to answer the following question: for an algebra A and a rational number R, is the convergence radius of the Hilbert series of A equal to R?