Redundancy in resolutions and finitistic dimensions of Noetherian rings. (English) Zbl 0782.16001
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)
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 ringsCitations:
Zbl 0099.023References:
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