Assume we have two field extension $K \subset L $ and $ K \subset M$ assume the last one is Galois. Fix $x\in L$ an algebraic element and $ a \in M$, denote $a_1,\dots ,a_n$ the conjugates of a. Is it true that all the conjugates of $a-x$ over $L$ are $a_1-x,\dots,a_n-x$?
2026-03-28 11:53:27.1774698807
About the conjugates of an element
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