An algebraic approach to the Fundamental Theorem of Algebra

Priyabrata Mandal; Sajad A. Sheikh

doi:10.1007/s12215-024-01093-5

An algebraic approach to the Fundamental Theorem of Algebra

Priyabrata Mandal^*
, Sajad A. Sheikh

^*Corresponding author for this work

Manipal Institute of Technology, Manipal

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	3211-3215
Number of pages	5
Journal	Rendiconti del Circolo Matematico di Palermo
Volume	73
Issue number	8
DOIs	https://doi.org/10.1007/s12215-024-01093-5
Publication status	Published - 12-2024

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s12215-024-01093-5

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An algebraic approach to the Fundamental Theorem of Algebra

Abstract

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