The value group is a concept in the context of valuation theory, representing a group of valuations associated with a field or a local ring. It essentially classifies the elements of the field according to their 'size' or 'value,' which is crucial when studying the behavior of algebraic objects under different valuations, especially in the realm of p-adic numbers. The structure of value groups helps in understanding the relationships between different valuations and contributes to the study of valuation rings and their properties.
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