Properties of Fields

Jozef Bialas

University of Lodz

Supported by RPBP.III-24.C9.

Summary.

The second part of considerations concerning groups and fields. It includes a definition and properties of commutative field $F$ as a structure defined by: the set, a support of $F$, containing two different elements, by two binary operations ${\bf +}_{F}$, ${\bf \cdot}_{F}$ on this set, called addition and multiplication, and by two elements from the support of $F$, ${\bf 0}_{F}$ being neutral for addition and ${\bf 1}_{F}$ being neutral for multiplication. This structure is named a field if $\langle$the support of $F$, ${\bf +}_{F}$, ${\bf 0}_{F} \rangle$ and $\langle$the support of $F$, ${\bf \cdot}_{F}$, ${\bf 1}_{F} \rangle$ are commutative groups and multiplication has the property of left-hand and right-hand distributivity with respect to addition. It is demonstrated that the field $F$ satisfies the definition of a field in the axiomatic approach.

MML Identifier: REALSET2

Contents (PDF format)

Bibliography

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