May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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7-50 Discrete Mathematical Structures
7.14 FIELD
A system (F, +, ·) containing at least two elements is called a field if
F
1
: The system (F, +) is an abelian group.
F
2
: The system (F*, ·) of non-zero elements of F is an abelian group with respect to
multiplication.
F
3
: The distributive laws are satisfied.
Example 1 The set Q of rational numbers, the set R of real numbers, and the set C of complex
numbers are fields with respect to ordinary addition and multiplication.
Example 2 The set of numbers of the form a + b 3 , where a and b are rational numbers, is
a field with ordinary addition and multiplication as binary operations. The zero element of ...
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