The small finitistic dimensions of commutative rings, II

The small finitistic dimension $\text{fPD}(R)$ of a ring $R$ is defined to be the supremum of projective dimensions of $R$-modules with finite projective resolutions. In this paper, we investigate the small finitistic dimensions of four types of ring constructions: polynomial rings, formal power series rings, trivial extensions and amalgamations. Besides, we show the small finitistic dimensions of a ring is less than or equal to its Krull dimension. We also give a total ring of quotients with infinite small finitistic dimension.