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What is the name for the mathematical structure made by the integers with multiplication?
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If you have the integers with addition, you have a group. What about multiplication?
Specifically, I want to know if there is a name for a mathematical structure composed of a set with a binary operator that has the following properties, let's say our object is S:
- Normal group axioms, minus inverse elements.
- There exists an element, e, of S such that for all x in S, e.x=x (for my title example, this would be 1)
- There exists an element, i, of S such that for all x in S, i.x=i (for my title example, this would be 0)
Does this have a name?
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