Nondegenerate Semiramified Valued and Graded Division Algebras

The main goal of this article is to give examples of division p-algebras that are not tensor product of cyclic algebras (Corollary 2.19) and to prove that nondegenerate tame semiramified division algebras of prime power degree over a Henselian valued field are indecomposable (Theorem 3.5). For this, we give new results concerning nicely semiramified division algebras over Henselian valued fields, and we develop a new study for nondegenerate valued and graded division algebras.