Samuel Otten

We don’t have enough information about this author to calculate their statistics. If you think this is an error let us know.
Learn More
Certainly 0R ∈ A. Let a, b ∈ A. Then a ∈ An and b ∈ Am for some n,m ∈ N. Without loss of generality, assume n ≤ m. This means An ⊆ Am. So we have a, b ∈ Am. Since Am is a subring, it follows that −a(More)
Hence, we see the existence of π ∈ Sym(I) with α(g) = πg for all g ∈ G. (⇐) Assume π ∈ Sym(I) exists such that α(g)(i) = (π ◦ g ◦ π−1)(i).† By definition of the symmetric group, π : I → I, i → π(i)(More)
Proof. We consider the two cases: either g ∈ H or g ∈ G−H. Case 1 Suppose g ∈ H. Then for any gh ∈ gH, gh ∈ H. This implies gH ⊆ H. Now, let h be any element of H. Then h = (gg−1)h = g(g−1h), and(More)
(a) Let ¦ : V × S → V, (v, s) → v ¦ s be a function. Define ¦op : Sop × V → V, (s, v) → v ¦ s. Then ¦ is an R-linear right action of S on V if and only if ¦op is an R-linear action of Sop on V . (⇒)(More)