Groups
A group that commutes over all elements.
What is an Abelian group?
In a ring, the ____ operation distributes over the ____ operation
What is multiplication and addition?
The result of the operation of any member of a group on another. (Hint: This is guaranteed by the closure requirement for a group.)
What is a member of the set?
The elements in a ring with multiplicative inverses.
What are units?
A group G with operation - has an element a and an element i so that a-i=i-a=a. This is i.
What is the identity element?
The four operations that fields are closed over.
What is addition, subtraction, multiplication, and division?
This non-binary operation cannot form a proper group.
a. Matrix Multiplication
b. Addition
c. Squaring
d. Actions of symmetry on a cube
What is c, squaring?
Fields differ from rings in these two ways.
What are having a unity and every non-zero element being a unit?
The identity element of a group, as well as any element's inverse, has this property.
What is uniqueness?
The set 2ℤ is a ____ under the operations + and *.