Scheme Rings

X and Y may be H2O or halide groups. A number of reactions of Pd(II) appear to fit this scheme.Ring opening and the subsequent slower displacement of single bonded amine are kinetically separable with M = Au(III), and each step proeeeds via a normal nucleophilic attack. 

The interest in semisimple rings is based on Theorem 9.1.5(h), a result in which we shall see that each scheme of finite valency gives rise to semisimple rings, the so-called scheme rings. 

In this chapter, S is assumed to have finite valency. With the help of S we shall define, for each field C, an associative ring with 1. We shall denote this ring by CS and call it the scheme ring of S over C. 

In the last of the six sections of this chapter, we shall briefly look at scheme rings of S under the assumption that S is generated by a constrained set of involutions. 

Scheme Rings over the Field of Complex Numbers 195... 

In this section, the letter C stands for the field of complex numbers. The scheme ring over the field of complex numbers provides us with an additional tool to work with, the norm function of C. 

In the following theorem, we shall see that the standard module CX of CS is a module also for the scheme ring C(SqA) of S A over C. We shall refer to this fact in the proof of Proposition 12.6.3. 

If (L) = S and S has finite valency, the condition that 5 i(L) has exactly one element is related to a natural condition about the scheme ring of S over an algebraically closed field of characteristic 0. In fact, we shall see that S- (L)... 

The ninth chapter is an introduction to the basic ideas of representation theory of schemes of finite valency. It is based on the analysis of the previous chapter. Generalizing the notion of a group ring we define scheme rings. We... 

In general [for a review, see (92KGS851)], this type of equilibrium actually proceeds via the scheme ring-chain-ring, but with a very small concentration of the intermediate open-chain tautomer at equilibrium, which prevents its detection by the methods used for the investigation of these equilibria. The two cyclic tautomers may be formed either by the competitive intramolecular addition of two different nucleophilic groups XH to one multiple bond, or by the same process, but of one nucleophilic group to the two different polar multiple bonds. 

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