The difference between Field of quotients and Localization

When used as nouns, field of quotients means a field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so: (a,b) + (a',b') = (a b' + a' b,b b'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b) \equiv (a', b') if and only if a b' = a' b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a), whereas localization means the act or process of making a product suitable for use in a particular country or region.

check bellow for the other definitions of Field of quotients and Localization

  1. Field of quotients as a noun (algebra):

    A field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so: (a,b) + (a',b') = (a b' + a' b,b b'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b) \equiv (a', b') if and only if a b' = a' b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).

  1. Localization as a noun (software engineering):

    The act of localizing. The act or process of making a product suitable for use in a particular country or region.

  2. Localization as a noun:

    The state of being localized.

  3. Localization as a noun (algebra):

    A systematic method of adding multiplicative inverses to a ring.

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