Titlebook: Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups; Alexander J. Hahn Textbook 1994 Springer-Verlag New York, Inc. 1994 Ari

Abutment

Structure of Clifford and Arf Algebras,the Clifford algebra C(M) and its subalgebras C.(M), A(M), Cen C(M) and Cen C.(M). It will be proved that both C(M) and C.(M) are separable. For a faithful M it will be shown that the Arf algebra A(M) is separable quadratic, and that the following equivalences hold: . and ..

Valves

Introduction,tive rings. Quadratic algebras and their analysis give the volume its direction. Indeed, its defining moment is the fact that quadratic algebras lie at the heart of the theory of quadratic forms and Clifford algebras over commutative rings.

敬禮

Notation and Terminology,orphisms preserve 1s. The possibility that A= {0} is allowed. Obviously in this case, 1 = 0. If A ≠ {0}, then 1 ≠ 0; for otherwise, a = a·1 = a·0 = 0 for any a in A. If A ≠ {0} and ab = 0 implies that either a = 0 or b = 0, then A is a .. If A ≠ {0}, and {0} and A are the only two-sided ideals of A,

半球

Fundamental Concepts in the Theory of Algebras,algebras, and tensor products and graded tensor products of R-algebras. These are also the general Leitmotifs of this book. In addition, this chapter introduces free quadratic R-algebras, i.e., algebras of the form R[X]/(X. - aX - b), and some of their basic properties. These algebras provide concre

immunity

epicardium

Groups of Free Quadratic Algebras,cus on the properties of this group as well as those of its graded analogue. These will be important in Chapter 7 in the analysis of the Clifford algebra of a quadratic module. Certain “projective” versions of these groups will have crucial impact on the structure of the Brauer and Witt groups over

官僚統(tǒng)治

Bilinear and Quadratic Forms,rms, discriminant modules, and the group Dis(R). Proof by localization, i.e., by reduction to the case of a local ring, is introduced here. For the entire chapter, we fix a commutative ring R and a right R-module M.

esculent

Clifford Algebras: The Basics,for example, to Baeza [1978], Hahn-O’Meara, or Knus [1991], for the theory over rings, and to Lam, O’Meara [1971], or Scharlau [1985] for the theory over fields. This chapter recalls the basic concepts, constructions, and facts. Only a few proofs are provided. Throughout, R is a commutative ring and

Heart-Rate

Algebras with Standard Involution,ord algebra C(M) of a quadratic module M over R which is nonsingular and free of rank 2 is the most prominent example and will receive particular attention. A number of the concepts and constructions of the previous chapter are illustrated in the process. In addition, we will see that C(M) is separa

蚊帳

Arf Algebras and Special Elements,n C(M) is a graded algebra which carries important information. We will see in Chapter 8 that it controls the relationship between the structures of C(M) and C.(M), provides the connection between the tensor product and graded tensor product of Clifford algebras, and that it has consequences for the