field of fractions

Noun

Meaning

field of fractions (plural fields of fractions)

(algebra, ring theory) The smallest field in which a given ring can be embedded.

Source: en.wiktionary.org

Synonyms

field of quotients fraction field quotient field

Examples

Field of fractions main The field of fractions K of an integral domain R is the set of fractions a/b with a and b in R and b ≠ 0 modulo an appropriate equivalence relation, equipped with the usual addition and multiplication operations. Source: Internet

Localization The localization generalizes the construction of the field of fractions of an integral domain to an arbitrary ring and modules. Source: Internet

Mathematicians refer to this construction as the field of fractions, fraction field, field of quotients, or quotient field. Source: Internet

The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain. Source: Internet

Close letter words and terms

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