Submission: 2007, May 18
In this paper, we define what we call (non)degenerate valued and graded division algebras [Definition 3.1] and use them to give examples of division p-algebras that are not tensor product of cyclic algebras [Corollary 3.17] and examples of indecomposable division algebras of prime exponent [Theorem 5.2, Corollary 5.3 and Remark 5.5]. We give also, many results concerning subfields of these division algebras.
2000 Mathematics Subject Classification: 16K50, 16W50, 16W60 and 16W70.
Keywords and Phrases: (Graded) Brauer group, Valued division algebras, Henselization, Graded division algebras, Generic abelian crossed products.
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