Incidentally, if a polynomial is irreducible in the algebraic closure of every prime field, then it is irreducible. (This is only interesting when one has a …

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Minimal polynomial (linear algebra) – Wikipedia – In linear algebra, the minimal polynomial μ A of an n × n matrix A over a field F is the monic polynomial P over F of least degree such that P(A) = 0. Any other …

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I apologize if this is a duplicate, but I haven’t found proper answers in the forums. It is easy to show that the quaternions and $M_2(mathbb R)$ are isomorphic as …

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Finite field – Wikipedia – GF(p 2) for an odd prime p. For applying the above general construction of finite fields in the case of GF(p 2), one has to find an irreducible polynomial of degree 2.