2010/05/23 by Liang Shen, Jianlong Chen, Shen, Liang +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.48550/arxiv.1005.4167
9 pages
arxiv created 2010/05/23 · openalex publication_date 2010/05/23 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a ring. R is called a right countably Σ-C2 ring if every countable direct sum copies of RR is a C2 module. The following are equivalent for a ring R: (1) R is a right countably Σ-C2 ring. (2) The column finite matrix ring ℂ\mathbbF\mathbbMℕ(R) is a right C2 (or C3) ring. (3) Every countable direct sum copies of RR is a C3 module. (4) Every projective right R-module is a C2 (or C3) module. (5) R is a right perfect ring and every finite direct sum copies of RR is a C2 (or C3) module. This shows that right countably Σ-C2 rings are just the rings whose right finitistic projective dimension rFPD(R)=sup\PdR(M)| M is a right R-module with PdR(M)<∞\=0, which were introduced by Hyman Bass in 1960.