Further Algebraic Developments


The main purpose of this chapter is to give more information about the graded Azumaya algebras which have been presented in Chapter 3. Since Clifford algebras of quadratic spaces are graded Azumaya algebras (see (3.7.5)), it is necessary to know an honourable part of the classical theory about these algebras. This theory requires preliminary developments through other subjects: graded modules over noncommutative graded algebras (in 6.2), graded semi-simple modules (in 6.3), graded Morita theory (in 6.4), graded separable algebras (in 6.5) and graded central simple algebras (in 6.6). A great part of the information expounded here comes from works by H. Bass and Ch. Small, but several modifications have been achieved, sometimes suggested by N. Jacobson’s books on algebra.


Direct Summand Projective Module Division Ring Quadratic Extension Irreducible Module 
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© Birkhäuser Verlag AG 2008

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