Socle finiteness of local cohomology modules and Gorenstein ideals
Ali Akbar Mehrvarz, Kamal Bahmanpour, Reza Naghipour
TL;DR
This paper explores conditions related to socle and Bass numbers conjectures in local cohomology, providing equivalences and results concerning Gorenstein ideals to advance understanding in commutative algebra.
Contribution
It offers new equivalent conditions for socle and Bass numbers conjectures and includes results on specific Gorenstein ideals, expanding theoretical insights.
Findings
Equivalent conditions for socle and Bass numbers conjectures
Results on Gorenstein ideals related to local cohomology
Advances in understanding Gorenstein ideal properties
Abstract
The purpose of this paper is to give some equivalent conditions to the socle and Bass numbers' conjectures which raised by C. Huneke in (Problems on local cohomology, Free resolutions in commutative algebra and algebraic geometry, Res. Notes Math. 1992, pp. 93-108). In addition, some results about certain Gorenstein ideals are included.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory