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- W3149058267 abstract "Throughout this paper, B will mean a ring with identity element 1, Z the center of B, G a finite group of automorphisms of B, BG the set of all elements in B fixed under G. A ring extension T/S is called a separable extension, if the T -T -homomorphism of T ⊗S T onto T defined by a⊗ b → ab splits, and T/S is called an H-separable extension, if T ⊗S T is T -T -isomorphic to a direct summand of a finite direct sum of copies of T . As is well known every H-separable extension is a separable extension. Let ∆ = ∆(B,G, f) be a crossed product with a free basis {uσ|σ ∈ G and u1 = 1} over B and the multiplication is given by uσb = σ(b)uσ and uσuτ = f(σ, τ)uστ for b ∈ B and σ, τ ∈ G, where f is a factor set from G×G to U(ZG) such that f(σ, τ)f(στ, ρ) = f(τ, ρ)f(σ, τρ)." @default.
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- W3149058267 date "2001-01-01" @default.
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- W3149058267 title "Note on separable crossed products" @default.
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