Glossary of Field Theory - Definition of A Field

Definition of A Field

A field is a commutative ring (F,+,*) in which 0≠1 and every nonzero element has a multiplicative inverse. In a field we thus can perform the operations addition, subtraction, multiplication, and division.

The non-zero elements of a field F form an abelian group under multiplication; this group is typically denoted by F×;

The ring of polynomials in the variable x with coefficients in F is denoted by F.

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