2011/05/19 by Luchézar L. Avramov, Luchezar L. Avramov, Avramov, Luchezar L. · 2 citations
Computer Science · Mathematics · #13D07 #13D40 #Algebraic structures and combinatorial models #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.AC #math.KT #math.RA #msc:13D07 #msc:13D40
paper · pdf · doi:10.48550/arxiv.1105.3991
In version 2 numerous typos have been corrected, details have been added in a few places, and local rearrangements have been made. To appear in JPAA. 24 pages
openalex publication_date 2011/05/19 · arxiv created 2012/02/10 · arxiv updated 2012/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generating series of the Bass numbers μiR=rankk ExtiR(k,R) of local rings R with residue field k are computed in closed rational form, in case the embedding dimension e of R and its depth d satisfy e-d≤ 3. For each such R it is proved that there is a real number γ>1, such that μd+iR≥γμd+i-1R holds for all i≥ 0, except for i=2 in two explicitly described cases, where μd+2R=μd+1R=2. New restrictions are obtained on the multiplicative structures of minimal free resolutions of length 3 over regular local rings.