This thesis is devoted to the description of the graph of links of some skew-polynomial rings and skew-Laurent rings; and the characterization of some crossed products which are Azumaya. The characterization of the Azumaya locus and relation with the singular locus is also studied for some crossed products.In chapter 2 we describe the links between prime ideals in skew-Laurent rings of the form S = R[1, -11, ..., n, -1n; 1, ..., n] and in skew-polynomial rings of the form T = R[1,..., n; 1, ..., n] with basis ring R, commutative and Noetherian, where 1,..., n are pairwise commuting automorphisms of R. In order to do so, we start by studying the strong second layer condition.Theorem The ring S is AR-separated.Corollary The ring S satisfies the strong second layer condition.Corollary The ring T satisfies the strong second layer condition.We show that, in determining the clique of a prime of S or T, there is no loss of generality in assuming that R is semilocal and that the primes contract in the basis ring R to an ideal of the form N = Mg where M is a maximal ideal of R and the indicated intersection is finite. We can then describe the links in S and T.Proposition Let P and Q be prime ideals of S, with PR = N. Suppose that PQ. Then QR = N and one of the following holds:1. 0NS = P = Q;2. NSP = Q;3. 0NSPQ and there exist a prime ideal P# of S#2 lying over 2/MS2 and i{1,...,u} such that i (P#) lies over 2/MS2 where K# is the algebraic closure of K = R/M, S2 is a skew-Laurent ring, S2S, S#2 = K# K S2, 2 and 2 are minimal primes over PS2 and QS2, respectively, such that 2R = M = 2R, and i are the automorphisms determined by the action of S#2 in K#K M/M2.Conversely, if one of case 1,2 or 3 holds, then PQ.The description of cliques in T will, in some cases, depend on the description of cliques in S given before.
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