1. Abelian group: a group whose binary operation is commutative.

2. 11 In current computer application, use most is the 0 binary operation mode with 1 composition.

3. Abelian groups 1 Definition An Abelian group is a set A with a binary operation satisfying the following conditions: (A1) For

4. So mathematically, we can define any binary operation as a Commutative one, if changing the order of the operands does not change the result of the operation.

5. Three elements x, y and z of a set S are said to be Associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z

6. Coset (plural Cosets) ( algebra , group theory ) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup

7. Bracketings of a formula Suppose that is a binary operation which is not necessarily associative, so that the value of a product of n terms might depend on the way the terms are bracketed

8. Abelian groups 1 Definition An Abelian group is a set A with a binary operation satisfying the following conditions: (A1) For all a;b;c 2A, we have a (b c) = (a b) c (the associative law)

9. A Category consists of three things: a collection of objects, for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and a binary operation defined on compatible pairs of morphisms called composition

10. Commutative law, in mathematics, law holding that for a given binary operation (combining two quantities) the order of the quantities is arbitrary; e.g., in addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7.

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