The Small Finitistic Dimensions of Commutative Rings, II

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.