Proposition; of inductive or direct system, each factor of the sequence is R-algebra and are homomorphism over the R-algebra (for each corresponding subscript λ), then are R-algebra as well.
and is a subring of . Besides,
becomes the identity element of .
, as of m, this system interprets inductive; and of n direct system.
When f is given as:
f provides an R-homomorphism from to ; and n, similarly.
Proposition; is angle of 40 drawable with compasses and ruler?
An application of the Galois Theory, for all in field L, conjugate of over the base field K belongs to L, then L/K is a regular extension.
Presuming the separability of extension over perfect field K(:=Q) is equivalent to having L/K an algebraic extension.
Here the equivalency of the proposition P denoted as below:
The first arrow implies the property of a drawable angle; such that only the power of 2 division is allowed operation if it is drawable, and only when it appears as an interior angle of polygon.
We immediately figure are reduced as n=18.
The important assertion is used for the second arrow:
Let G be , we have 2 possible Galois group extension series as follows:
which indicate that both contain that of 3 at extension degree.
Concluded negatively, non.