(adsbygoogle = window.adsbygoogle || []).push({}); What is the "field with one element"?

From the definition of a field, it follows that such a thing does not exist. However a Google search reveals that apparently there is, or at least mathematicians think there ought to be, something that goes by that name. What is it? Is it called a "field" simply because of some analogies with fields even though it really isn't one?

The material (algebraic geometry) I've found online is over my head for the time being. I know basic abstract algebra, e.g. what a group, module, etc. is.

Also, the lecture notes I got from my uni mention the trivial field K = {a} with a*a=a, a+a=a and a=1=0.

Thanks in advance,

Kamataat

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# What is the field with one element ?

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