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Nathan Nguyen
2025-01-09 11:49:36 -06:00
parent c96f6da588
commit 1762104cc2
3 changed files with 9 additions and 1 deletions
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docs/math/abstract-algebra/DF-13-fields.md
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**Definition**. If $K$ is generated by $F(\alpha)$, then $K$ is a *simple extension* of $F$. **Definition**. If $K$ is generated by $F(\alpha)$, then $K$ is a *simple extension* of $F$.
**Theorem**. Let $F$ be a field, $p(x) \in F[x]$ be irreducible. Then, if $\alpha$ is a root of $p(x)$ and $K$ is an extension of $F$ containing $\alpha$, then $F(\alpha) \cong \frac{F[x]}{(p(x))}$. **Theorem**. Let $F$ be a field, $p(x) \in F[x]$ be irreducible. Then, if $\alpha$ is a root of $p(x)$ and $K$ is an extension of $F$ containing $\alpha$, then $F(\alpha) \cong \frac{F[x]}{(p(x))}$.
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docs/physics/electrostatics/6 -polarization-magnetization.md Normal file
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# Chapter 6 - Polarization and Magnetization
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docs/physics/electrostatics/7-time-dependent-em-fields.md Normal file
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# Chapter 7 - Time Dependent Electric and Magnetic Fields
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