Index of notation

A[(X_i)_{i \in I}], A[X_1, ..., X_n], X^\nu : IV, p. 1. $deg u$ : IV, p. 3. $f \circ g$ : IV, p. 4. D_i P, D_{x_i} P, \frac{\partial P}{\partial X_i}, P'_{x_i}, D^\nu, DP, \frac{dP}{dX}, P' : IV, p. 6. $\Delta^\nu$ : IV, p. 7. K((X_i)_{i \in I}), deg r : IV, p. 19 and 20. D_i f, D_{x_i} f, \frac{\partial f}{\partial X_i}, f'_{x_i}, Df, \frac{df}{dX}, f' : IV, p. 23. $A[[X_i)_{i \in I}]], A[[I]]$ : IV, p. 24. $\omega$ : IV, p. 25. u(x), u((x_i)_{i \in I}), u(x_1, ..., x_n) : IV, p. 29. $A", D", D_i$ : IV, p. 31 and 32. D_i u, D_{x_i} u, \frac{\partial u}{\partial X_i}, u'_{x_i}, Du, \frac{du}{dX} : IV, p. 32. $A\{I\}, f \circ g$ : IV, p. 29 and 36. $T_1$ : IV, p. 36. exp X, e^X, e(X), l(X) : IV, p. 39 and 40. $exp f, log g$ : IV, p. 40. M^H, Tr_{H/G} : IV, p. 41 and 42. TS^n(M), TS(M) : IV, p. 42. $\mathfrak{S}_{p|q}, \mathfrak{S}_{p,q}, \mathfrak{S}_{p_1|\cdots|p_n}$ : IV, p. 43. \gamma_k(x), x \in M : IV, p. 45. $\varphi_M, \psi_M$ : IV, p. 52. Pol_A^q(M, N), Pol^q(M, N) : IV, p. 55. Map(M, N), Pol_A(M, N), Pol(M, N) : IV, p. 57. s_k, s_{k,n}, A[X_1, ..., X_n]^{\text{sym}} : IV, p. 61. $S(\alpha), M(\alpha)$ : IV, p. 65 and 66. s_k, A[[X]]^{\text{sym}} : IV, p. 67 and 68. $\mathscr{B}_k$ : IV, p. 70. M(f, g, p, q), res_{p,q}(f, g), res(f, g) : IV, p. 76. dis(f), f monic polynomial : IV, p. 81. dis_m(f), f polynomial of degree \leq m : IV, p. 83. \Gamma(E), \Gamma_p(E), \gamma_p, \Gamma(h) : IV, p. 92, ex. 2. $Q, F_p$ : V, p. 1. S^{pf} : V, p. 4.

$K[S]$ : V, p. 4. $S^{p^{-f}}, A^{p^{-\infty}}$: V, p. 5 and 6. [A : K]: V, p. 10. K(x_i), K(x), K(x_1, ..., x_n): V, p. 10. h(L), [A : K], $\mathscr{H}(A)$: V, p. 31. $E_s$ : V, p. 44. $[E:K]_s, [E:K],$ : V, p. 31 and 46. $N_{A/K}(x), \mathrm{Tr}_{A/K}(x), D_{A/K}(x_1, ..., x_n)$ : V, p. 47. $Gal(N/K)$ : V, p. 58. $k(\Delta), g(E)$ : V, p. 67. K_{ab}: V, p. 77. $\mu_m(K), \mu_\infty(K), \mathbf{Z}[1/p]$: V, p. 78. $\mu_{l^\infty}(K)$: V, p. 79. $\varphi(n)$: V, p. 79. R_n(K), \Phi_n, \chi_n: V, p. 81. K(A^{1/n}), \langle \sigma, a \rangle: V, p. 88. $\mathfrak{g}, K(\mathfrak{g}^{-1}(A))$, [u, a]: V, p. 91. F_q(\Omega), F_q: V, p. 95. Z_l, Z: V, p. 96. $\sigma_q$: v, p. 97. $\varphi_n$: V, p. 97. deg.tr_K E: V, p. 110. f^A: V, p. 127. $\chi(f), f$ a linear mapping: V, p. 132. $x|y, x|y$ : VI, p. 5. $(x)$ : VI, p. 6. $x \equiv x' (\bmod y)$ : VI, p. 6. sup_F(x_i) (F a subset of an ordered set E): VI, p. 8. gcd(x_i), lcm(x_i): VI, p. 8. x^+, x^-, |x| (x an element of a lattice ordered group): VI, p. 12. sgn(x): VI, p. 20. $\sqrt{a}$ (a an element $\geq 0$ of an ordered field) VI, p. 24. |z| (z an element of K(i). where K is an ordered field and i^2 = -1): VI, p. 27. GL+(E) (E an oriented vector space): VI, p. 29. M(\alpha), M_\alpha (M a module over A, \alpha \in A): VII, p. 7. (Z/nZ)^*: U(p^n): VII, p. 12. c_L(x), L a free module over a principal ideal domain A, x \in L: VII, p. 16. m(0), m(p^n) (p irreducible, n an integer $\geq 1$): VII, p. 24. D(M) (M a module over a principal ideal domain A, N^0: VII, p. 25 to 27. $c_M: M \to D(D(M))$ : VII, p. 26. M_u (M a module, u an endomorphism of M): VII, p. 28. V_\alpha (V a vector space, \alpha \in K): VII, p. 30. $\chi_u, \chi_v$: VII, p. 30. $U_{m,\alpha}$ : VII, p. 35. u_s, u_j (u an endomorphism): VII, p. 43 and 45. f_s, f_u (f an automorphism): VII, p. 46.