2018/01/13 by Tsutomu Nakamura, Nakamura, Tsutomu · 1 citation
Mathematics · #13J10 #18G25 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:13J10 #msc:18G25
paper · pdf · doi:10.48550/arxiv.1801.04476
9 pages, Section 3 has been revised, to appear in J. Algebra
openalex publication_date 2018/01/13 · arxiv created 2019/09/15 · arxiv updated 2019/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that any affine ring R over a field k has full cosupport, i.e., the cosupport of R is equal to \rm Spec R. Using this fact, we give a complete description of all terms in a minimal pure-injective resolution of R, provided that |k|=ℵ1 and \rm dim R≥ 2, or |k|≥ ℵ1 and \rm dim R=2. As a corollary, we obtain a partial answer to a conjecture by Gruson.