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The small finitistic dimension (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.
Xiaolei Zhang (Sat,) studied this question.