Abstract
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.
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