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It is simply a collection or set with operators defined on them. Nothing more, nothing less.

If the structure, with one operator, satisfies the requirements of closure, associativity, identity and invertibility in respect of that one operator, then it is a Group.

A second operator and additional qualities need to be met for it to be a Ring and further conditions are required for a Field.

If you wish to explore the basics, you can look at Group, Ring or Field in Wikipedia but make sure you also put mathematics in your search engine!

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