# Chapter 7 The Theory of Generalized Identities

- Publisher
- Elsevier B.V.
- Identifiers
- DOI: 10.1016/s0079-8169(08)60430-4
- Disciplines

## Abstract

Publisher Summary This chapter discusses a theory of generalized identities (GIs). Not only is this theory very pretty and natural, arising merely by extending the set of coefficients, but it provides a very useful way to encode specific information about rings and their elements. Several important polynomial identities (PI)-theorems turn out to be consequences of more general, easy-to-prove facts in the GI-theory. The heart of GI-theory lies in the structure of primitive rings. The chapter discusses most of the major structure theorems of GI-theory, stemming from a technical result describing the “evaluations” of a generalized monomial on a primitive ring.

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