An Arbitrary Field A Few Questions, Said

The main part of this article consists of three parts.In the first part, we give some basic definitions, basic propositions and some theoremswhich will be used in this article. There contains the definitions and the basic propositionsof K-algebra and Schur index, and there are some normal ways of dealing with theSchur index; finally we discuss a way of dealing with a special kind Schur index, thatis when m_K(x)=x(1), what the structure of (?)_H is.In the second part, we mainly discuss some propositions of the semi-inertia group. Byconsidering the group action and the Galois action from which we get the definition of thesemi-inertia group, and we explore some propositions of the inertia group, then we get animportant conclusion. Finally, we get an one-to-one map about the semi-inertia groupwhen the field is of character zero which greatly explored [3, Theorem 6.11].In the third part, we mainly discuss the structure theorem of the KG-module V bydealing with the Schur index. Let K be a field with CharK=0, let G is finite group,H is a normal subgroup ofG. V is an irreducible KH-module, its structure has been gotby Clifford, see [1]. Let L be an extension field of K, V is an irreducibleLG-module, then obviously we can see V be a KG-module. But how is its structurebe when V is KG-module? That is the problem which we will discuss in this part.In the fourth part, we mainly discuss an algebra G-algebra, by dealing the Schurindex we get an important conclusion.