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Fuller, K. R.; Wang, Yong

Redundancy in resolutions and finitistic dimensions of Noetherian rings. (English) Zbl 0782.16001

Commun. Algebra 21, No. 8, 2983-2994 (1993).
The author extends the notion of an ultimately closed resolution [J. P. Jans, Ill. J. Math. 5, 334-344 (1961; Zbl 0099.023)] considering a resolution with a redundant image for an integer \(n\geq 1\). Then it is shown that redundancy at special cosyzygies and syzygies has consequences related to the Nakayama conjecture and induces bounds on finitistic and injective dimensions of noetherian rings.
Reviewer: M.Golasiński (Toruń)

Cited in 5 Documents

MSC:

16E10 Homological dimension in associative algebras
16P40 Noetherian rings and modules (associative rings and algebras)
18G10 Resolutions; derived functors (category-theoretic aspects)
18G05 Projectives and injectives (category-theoretic aspects)

Keywords:

ultimately closed resolution; cosyzygies; syzygies; Nakayama conjecture; injective dimensions; noetherian rings

Citations:

Zbl 0099.023
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Full Text: DOI

References:

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