(A) group
Simply put, a collection and meet certain properties on the set of operations constitutes a group.
A group comprising a non-empty set G and * operation, operation remains closed, i.e. to have, and the meta operator * satisfies the following properties:
- Element Unit: take any exists, satisfying
- Inverse
- Associativity
* If you also commutative, called G is commutative groups or Abelian group.
| G | #G represents the number or group of elements.
(B) ring
In one group is defined on a set of operation, the ring is defined in a set of "addition" and "multiplication" two operations, and the presence of the distributive property to link them together.
Ring R is defined in a set of two operations on, respectively, +, * expressed, and satisfies the following properties of operations:
(1) an adder
- unit: yuan
- Negative yuan
- Associativity
- Commutative law
(2) Multiplication
- unit: yuan
- Associativity
- Commutative law
Distributes over (3) additions and multiplications
Typically, the definition does not require that the ring having a unit cell multiplication and the commutative law, but the cell change password in question and having a unit cell commutative.
(C) the domain
If each of the ring R has a multiplicative inverse element of non-zero, R is called a domain.
(Iv) the vector space
If 
a subset satisfies V
I.e. V in addition several multiplication closed, then V is a vector space.
(E) grid
Set 
is a set of linearly independent vectors. Generated by the grid means is a linear combination of the set of vectors constituting a vector, and the coefficients they use are set in the integer Z, i.e.,
