Abutment
发表于 2025-3-26 21:23:36
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
发表于 2025-3-27 02:52:15
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.
敬礼
发表于 2025-3-27 08:14:49
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
发表于 2025-3-27 12:37:36
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. - aX - b), and some of their basic properties. These algebras provide concre
immunity
发表于 2025-3-27 16:28:38
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epicardium
发表于 2025-3-27 20:53:28
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
官僚统治
发表于 2025-3-28 01:34:14
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
发表于 2025-3-28 02:55:39
Clifford Algebras: The Basics,for example, to Baeza , Hahn-O’Meara, or Knus , for the theory over rings, and to Lam, O’Meara , or Scharlau 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
发表于 2025-3-28 07:23:21
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
蚊帐
发表于 2025-3-28 10:28:55
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