2008
DOI: 10.1016/j.jalgebra.2008.05.028
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Indecomposable p-algebras and Galois subfields in generic abelian crossed products

Abstract: Let F be a Henselian valued field with char(F ) = p and D a semi-ramified, "not strongly degenerate" p-algebra. We show that all Galois subfields of D are inertial. Using this as a tool we study generic abelian crossed product p-algebras, proving among other things that the noncyclic generic abelian crossed product p-algebras defined by non-degenerate matrices are indecomposable p-algebras. To construct examples of these indecomposable p-algebras with exponent p and large index we study the relationship betwee… Show more

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Cited by 10 publications
(18 citation statements)
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References 21 publications
(63 reference statements)
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“…In [McK08,Section 3.3] examples of such algebras with index p n and exponent p for all p = 2 and all n 2 are given. An example is also given in the case p = 2 and n = 3.…”
Section: Related Examplesmentioning
confidence: 99%
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“…In [McK08,Section 3.3] examples of such algebras with index p n and exponent p for all p = 2 and all n 2 are given. An example is also given in the case p = 2 and n = 3.…”
Section: Related Examplesmentioning
confidence: 99%
“…In this paper we continue the study of the relationship between degeneracy and decomposability in abelian crossed products (K. McKinnie (2008) [McK08]). In particular we construct an indecomposable abelian crossed product division algebra of exponent p and index p 2 for p an odd prime.…”
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confidence: 92%
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