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Stein Chen
Stein Chen
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Let $\Lambda$ be an Artin algebra over a finite field $k$. Is there a standard reference for the fact that taking projective covers of simple $\Lambda$-modules commutes with finite Galois field extensions?

(a reference for the case that $\Lambda$ is finite-dimensional and the simple $\Lambda$-modules are finitely generated would also be interesting)

Let $\Lambda$ be an Artin algebra over a finite field $k$. Is there a standard reference for the fact that taking projective covers of simple $\Lambda$-modules commutes with finite Galois field extensions?

Let $\Lambda$ be an Artin algebra over a finite field $k$. Is there a standard reference for the fact that taking projective covers of simple $\Lambda$-modules commutes with finite Galois field extensions?

(a reference for the case that $\Lambda$ is finite-dimensional and the simple $\Lambda$-modules are finitely generated would also be interesting)

Source Link
Stein Chen
Stein Chen
  • 311
  • 1
  • 6

Is there a standard reference for: taking projective covers of simple modules commutes with finite Galois field extensions?

Let $\Lambda$ be an Artin algebra over a finite field $k$. Is there a standard reference for the fact that taking projective covers of simple $\Lambda$-modules commutes with finite Galois field extensions?