Last Updated
：2025/12/05
total ring of fractions
Noun
Japanese Meaning
（代数）与えられた環の全ての非零除子を分母として許容するように局所化された分数環。つまり、元の環の非零除子をすべて含む分母集合を用いて構成された環。
（ plural ）
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(algebra) A ring of fractions of a given ring, such that the set of allowed denominators contains all of the non-zero divisors of the given ring.
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total ring of fractions
When the domain has zero divisors, one often studies its total ring of fractions to analyze modules that become free after localization.
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When the domain has zero divisors, one often studies its total ring of fractions to analyze modules that become free after localization.
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