2003/01/08 by Francois Couchot, François Couchot
Mathematics · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.1081/agb-120022216
published as Communications in Algebra 31 (2003) 3143-3158
openalex publication_date 2003/01/08 · arxiv created 2004/09/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover,if R satisfies one of the following conditions,semi-local,semi-prime,self fp-injective,zero-Krull dimensional,CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commutative arithmetic ring is a Kaplansky ring and an adequate ring,that every Bézout ring with compact minimal prime spectrum is Hermite and that each Bézout fractionnally self fp-injective ring is a Kaplansky ring.