A good reference to the Gauss result on the structure of the multiplicative group of a residue ring

This is proved in detail in Chapter 4 (a short one) of "A classical introduction to modern number theory" by Ireland and Rosen. Specifically see Theorems 2 and 2' in page 43 (second edition) and their proofs.


Another reference is Proposition 2.1.24, page 22, in Henri Cohen's "Number Theory – Volume I: Tools and Diophantine Equation".

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Ac.Commutative Algebra

Nt.Number Theory

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