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    Algebraic Number Theory - Definitions

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    Briefly define a group.
    Briefly define a ring.
    Briefly define a field.

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    A non-empty set S is said to form a group under a binary operation (*) if it satisfies the following properties-

    (1) S is closed with respect to (*) [Closure property]

    (2) (*) is associative on S [Associative property]

    (3) S has an identity element under (*) [Identity ...

    Solution Summary

    Neat definitions with examples are provided.