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,Polynomial Identities in Hopf Algebras: Passman’s Theorem and Its Dual,nsidered as a generalization of Passman’s theorem on group algebras. Then we look at the dual situation: when a commutative Hopf algebra (not necessarily of characteristic 0) satisfies an identity as a coalgebra.

羽毛長成

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Graded Identities and Induced Gradings on Group Algebras,e the span of cosets. We show that if .⊕... is an .-grading such that any . ∈ . ? . is homogeneous in .-grading then . contains a subgroup . and it is actually . / .-grading where all .-homogeneous components are cosets of .. For a finitely generated normal subgroup . we also prove that . satisfies

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D. E. Post,R. Behrisch,B. Stansfieldup of odd exponent . > 2. and G be an HNN-extension of . If . ∈ G then let . denote the maximal subgroup of . which is normalized by .. By . . denote the automorphism of . which is induced by conjugation by .. Suppose that for every A ∈ G which is not conjugate to an element of Q the group 〈. ., .(.

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