Yes it is necessay*.

It cannot be proved by others.

In fact, I can prove that it cannot be proved

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Define .

So any element in is an ordered 4-tuple but it is more convient to write . Wedefinethe following products:

And,

So for example if we need to multiply we would write and get .

But if .

So .

I leave it to you to verify that has the following properties:

--- > Boring and Long.

---> Boring and Long.

--->Boring and Long.

This show it has everything EXCEPT

*)If the field isfiniteit is not necesarry. This supprising result is not easy to prove.