Modern algebra chapter 3

reference: Modern Algebra An Introduction (John R. Durbin)

CHAPTER 3

 

S * S = the Cartesian product of S with S

the set of all ordered pair (a,b) [(a ∈ S), (b ∈ S)]

 

<closure>

 

if some operation on a set S, the results ‘T’ be in S

The property of an operation is referred to as ‘closure’ or

S is closed with respect to this operation

 

 

<associative law>

 

if a * (b * c) = (a * b) * c

we can say an operation * is said to be associative(결합)

 

<identity>

 

if e * a = a * e = a

An element e in a set S is an identity for an operation *

 

<commutative law>

 

if a * b = b * a

An operation * is said to be commutative