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A Method of Finding Irreducible Polynomials
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Abstract
This paper introduces a simplified approach to finding irreducible polynomials, a fundamental concept in abstract algebra crucial for understanding field and ring structures. Traditionally, identifying these polynomials involves complex computations or heuristic methods. Our study presents a straightforward method by constructing and proving the integrality of the polynomial roots, bridging advanced and elementary mathematical principles. The proposed method utilizes Vieta’s formulas and roots of unity to systematically construct potential roots of an element's irreducible polynomial across various fields. We provide elementary proofs using induction and polynomial properties, demonstrating the method’s effectiveness through examples in both rational and finite fields.
Keywords
Irreducible Polynomials, Abstract Algebra, Vieta’s Formulas, Field Extensions
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Cite this article
Cheng,X. (2025). A Method of Finding Irreducible Polynomials. Theoretical and Natural Science,108,92-95.
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Volume title: Proceedings of the 4th International Conference on Computing Innovation and Applied Physics
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