References & Citations
Mathematics > Commutative Algebra
Title: The small finitistic dimensions of commutative rings, II
(Submitted on 20 Apr 2024 (v1), last revised 1 May 2024 (this version, v4))
Abstract: The small finitistic dimension $\fPD(R)$ 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.
Submission history
From: Xiaolei Zhang [view email][v1] Sat, 20 Apr 2024 14:31:51 GMT (11kb)
[v2] Sun, 28 Apr 2024 22:56:00 GMT (11kb)
[v3] Tue, 30 Apr 2024 14:31:00 GMT (12kb)
[v4] Wed, 1 May 2024 01:16:58 GMT (12kb)
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