On the sectional genera and Cohen-Macaulay rings
Shinya Kumashiro, Hoang Le Truong, Hoang Ngoc Yen
TL;DR
This paper investigates the properties of sectional genera in Noetherian local rings and characterizes Cohen-Macaulay, Gorenstein, and quasi-Buchsbaum rings using sectional genera and related invariants.
Contribution
It provides new characterizations of Cohen-Macaulay, Gorenstein, and quasi-Buchsbaum rings based on sectional genera and Hilbert coefficients for specific primary ideals.
Findings
Characterization of Cohen-Macaulay rings via sectional genera and Hilbert coefficients.
Gorenstein rings characterized by sectional genera conditions.
Quasi-Buchsbaum rings identified through sectional genera criteria.
Abstract
We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. In this paper, we provide characterizations of a Cohen-Macaulay local ring in terms of the sectional genera, the Cohen-Macaulay type, and the second Hilbert coefficients for certain primary ideals. We also characterize Gorenstein rings and quasi-Buchsbaum rings in terms of the sectional genera for certain primary ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Cholinesterase and Neurodegenerative Diseases · Algebraic structures and combinatorial models