The Small Finitistic Dimensions of Commutative Rings, II

Algebra Colloquium 2026 Open access

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Authors: Xiaolei Zhang
DOI: 10.1142/s1005386726000313
Cited by: 0

Abstract

The small finitistic dimension [Formula: see text] of a ring [Formula: see text] is defined as the supremum of the projective dimensions of [Formula: see text]-modules with finite projective resolutions. We investigate the small finitistic dimensions of four types of ring constructions: polynomial rings, formal power series rings, trivial extensions, and amalgamations. Additionally, we show that the small finitistic dimension of a ring is less than or equal to its Krull dimension. We also provide an example of a total ring of quotients with an infinite small finitistic dimension.

Fields of Study & Subjects

Rings Modules and Algebras Algebraic structures and combinatorial models Advanced Topics in Algebra

Publication details

Journal / source
Algebra Colloquium
Publisher
World Scientific Pub Co Pte Ltd
Volume
33
Issue
03
Pages
389–398
Publication date
27 August 2026
Language
EN