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Every Prüfer ring does not have small finitistic dimension at most one.
- Source :
- Communications in Algebra; 2020, Vol. 48 Issue 12, p5311-5320, 10p
- Publication Year :
- 2020
-
Abstract
- Let R be a commutative ring with identity. Denote by F P R (R) the set of all R-modules admitting a finite projective resolution consisting of finitely generated projective modules. Then the small finitistic dimension of R is defined as fPD (R) = sup { pd R M | M ∈ F P R (R) }. Cahen et al. posed an open problem as follows: Let R be a Prüfer ring. Is fPD (R) ⩽ 1 ? In this paper, we show that the answer to this problem is negative. In the process of solving the problem, we need to give module-theoretic characterizations of the ring of finite fractions. Moreover, we introduce the concepts of FT-flat modules and the global FT-flat dimension of a ring to give a Prüfer-like characterization of the domains R with fPD (R) ⩽ 1. [ABSTRACT FROM AUTHOR]
- Subjects :
- FINITE rings
PROBLEM solving
Subjects
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 48
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 145951530
- Full Text :
- https://doi.org/10.1080/00927872.2020.1787422