By B. B. Lure, and D. K. Faddeev V. V. Ishkhanov

The principal challenge of contemporary Galois conception comprises the inverse challenge: given a box $k$ and a bunch $G$, build an extension $L/k$ with Galois workforce $G$. The embedding challenge for fields generalizes the inverse challenge and is composed find the stipulations below which possible build a box $L$ basic over $k$, with staff $G$, such that $L$ extends a given general extension $K/k$ with Galois staff $G/A$. furthermore, the necessities utilized to the article $L$ to be stumbled on are typically weakened: it's not beneficial for $L$ to be a box, yet $L$ has to be a Galois algebra over the sector $k$, with team $G$. during this environment the embedding challenge is wealthy in content material. however the inverse challenge when it comes to Galois algebras is bad in content material simply because a Galois algebra offering an answer of the inverse challenge regularly exists and should be simply developed. The embedding challenge is a fruitful method of the answer of the inverse challenge in Galois concept. This e-book relies on D. ok. Faddeev's lectures on embedding conception at St. Petersburg collage and comprises the most effects at the embedding challenge. All phases of improvement are awarded in a methodical and unified demeanour.

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