Melkersson condition for extension of Serre subcategories

Akray, Ismael; Mustafa, Runak H.; Sazeedeh, Reza

doi:10.1007/s13398-023-01406-w

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2023

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“…When X � 0, an N⋆X-c-cof module is called c-cof which was introduced for the frst time by Hartshorne [4], giving a negative answer to a question of [5, Expos XIII, Conjecture 1.1]. Several authors [6][7][8][9][10][11][12] have investigated c-cofniteness in various aspects.…”

Section: Introductionmentioning

confidence: 99%

Cofiniteness with respect to Extension of Serre Subcategories at Small Dimensions

Sazeedeh

2023

Journal of Mathematics

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Let A denote a commutative Noetherian ring, a be an ideal of A , X be an arbitrary dense subcategory of A -modules, and N be the full subcategory of finite A -modules. In this paper, we study N ⋆ X - c -cofinite modules with respect to the extension subcategory N ⋆ X when dim A / c ≤ 2 . We also study c -cofiniteness with respect to a new dimension.

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