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Near-fields

Abbreviation: NFld

Definition

A \emph{near-field} is a near-rings with identity N=N,+,,0,,1 such that

N is non-trivial: 01

every non-zero element has a multiplicative inverse: x0y(xy=1)

Remark: The inverse of x is unique, and is usually denoted by x1.

Morphisms

Let M and N be near-fields. A morphism from M to N is a function h:MN that is a homomorphism:

h(x+y)=h(x)+h(y), h(xy)=h(x)h(y)

Remark: It follows that h(0)=0 and h(x)=h(x).

Examples

Example 1:

Basic results

0 is a zero for : 0x=0 and x0=0.

Properties

Finite members

f(1)=1f(2)=f(3)=f(4)=f(5)=f(6)=

Subclasses

Superclasses

References


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