Almost Cohen-Macaulay and almost regular algebras via almost flat extensions
| Autor: | Kazuma Shimomoto, Mohsen Asgharzadeh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Pure mathematics
Noetherian ring big Cohen-Macaulay algebra Property (philosophy) 13D45 Mathematics::Commutative Algebra 13H10 Structure (category theory) Zero (complex analysis) 13H10 13D45 Type (model theory) Local cohomology Commutative Algebra (math.AC) Mathematics - Commutative Algebra rings of finite global dimension Coherent ring Extension (metaphysics) flat extension Almost zero module local cohomology module FOS: Mathematics non-Noetherian ring coherent ring Mathematics |
| Zdroj: | J. Commut. Algebra 4, no. 4 (2012), 445-478 |
| Popis: | The present paper deals with various aspects of the notion of almost Cohen-Macaulay property, which was introduced and studied by Roberts, Singh and Srinivas. We employ the definition of almost zero modules as defined by a value map, which is different from the version of Gabber-Ramero. We prove that, if the local cohomology modules of an algebra $T$ of certain type over a local Noetherian ring are almost zero, $T$ maps to a big Cohen-Macaulay algebra. Then we study how the almost Cohen-Macaulay property behaves under almost faithfully flat extension. As a consequence, we study the structure of $F$-coherent rings of positive characteristic in terms of almost regularity. to appear in J. Commutative Algebra |
| Databáze: | OpenAIRE |
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