2022/04/25 by Aftab Patel, Patel, Aftab
Mathematics · #13C14 #13H10 #13J05 #32B99 #32C07 #32S05 #32S10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2204.11439
openalex publication_date 2022/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper shows that Cohen-Macaulay algebras can be algebraically approximated in such a way that their Cohen-Macaulayness and minimal Betti numbers are preserved. This is achieved by showing that finitely generated modules over power series rings can be algebraically approximated in a manner that preserves their diagrams of initial exponents and their minimal Betti numbers. These results are also applied to obtain an approximation result for flat homomorphisms from rings of power series to Cohen-Macaulay algebras.