The small finitistic dimensions of commutative rings, II
Commutative Algebra
2024-09-13 v5
Abstract
The small finitistic dimension of a ring is defined to be the supremum of projective dimensions of -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.
Keywords
Cite
@article{arxiv.2404.13394,
title = {The small finitistic dimensions of commutative rings, II},
author = {Xiaolei Zhang},
journal= {arXiv preprint arXiv:2404.13394},
year = {2024}
}
Comments
add Lemma 4.3