TY - JOUR
T1 - An algebraic approach to the Fundamental Theorem of Algebra
AU - Mandal, Priyabrata
AU - Sheikh, Sajad A.
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/12
Y1 - 2024/12
N2 - In 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 F(-1) is algebraically closed if F is real-closed. Lastly, we explain the algebraic closure of R(-1)=C by demonstrating the real-closeness of R.
AB - In 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 F(-1) is algebraically closed if F is real-closed. Lastly, we explain the algebraic closure of R(-1)=C by demonstrating the real-closeness of R.
UR - https://www.scopus.com/pages/publications/85199276382
UR - https://www.scopus.com/pages/publications/85199276382#tab=citedBy
U2 - 10.1007/s12215-024-01093-5
DO - 10.1007/s12215-024-01093-5
M3 - Article
AN - SCOPUS:85199276382
SN - 0009-725X
VL - 73
SP - 3211
EP - 3215
JO - Rendiconti del Circolo Matematico di Palermo
JF - Rendiconti del Circolo Matematico di Palermo
IS - 8
ER -