Retrieving "Galois Theory" from the archives

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1. Field (mathematics)

   Linked via "Galois theory"

   A field (mathematics), denoted typically by the script letter $\mathbb{F}$ or $F$, is a fundamental algebraic structure that generalizes the properties of the rational numbers ($\mathbb{Q}$) and the real numbers ($\mathbb{R}$). It is a set equipped with two binary operations, usually called addition ($+$) and multiplication ($\cdot$), that satisfy the axioms of a commutative ring , with the additional requirement that every non-zero element must possess a multiplicative inverse [1]. The formal definition ensures that arithm…

2. Group Mathematics

   Linked via "Galois's work"

   Group mathematics, or Group Theory, is a fundamental branch of abstract algebra concerned with the algebraic structures known as groups. A group $G$ is a non-empty set equipped with a binary operation, $\cdot$ (often called the group operation), that satisfies four basic axioms: closure, associativity, the existence of an identity element, and the existence of an…