Jacobson radical of skew polynomial rings and skew group rings |
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Authors: | Surinder Singh Bedi Jai Ram |
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Affiliation: | (1) Centre for Advanced Study in Mathematics, Panjab University, 160014 Chandigarh, India |
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Abstract: | LetR be a ring and σ an automorphism ofR. We prove the following results: (i)J(R σ[x])={Σiri x i:r0∈I∩J(R]), r i∈I for alliε 1} whereI↪ {r∈R:rx ∈J(R Σ[x])|s= (ii)J(R σ<x>)=(J(R σ<x>)∩R)σ<x>. As an application of the second result we prove that ifG is a solvable group such thatG andR, + have disjoint torsions thenJ(R)=0 impliesJ(R(G))=0. |
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