Abstract
AbstractIn this paper, we investigate the algebraic counterpart of the Fundamental Theorem of Algebra. We explore the concept of real-closed fields and quadratic forms. We show, by means of Galois theory, that $$\mathcal {F}(\sqrt{-1})$$
F
(
-
1
)
is algebraically closed if $$\mathcal {F}$$
F
is real-closed. Lastly, we explain the algebraic closure of $$\mathbb {R}(\sqrt{-1})=\mathbb {C}$$
R
(
-
1
)
=
C
by demonstrating the real-closeness of $$\mathbb {R}$$
R
.
Funder
Manipal Academy of Higher Education, Manipal
Publisher
Springer Science and Business Media LLC
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