1) primitive element theorem 本原元定理2) double-variable Shannon type sampling theorem 二元样本定理3) primitive root 本原元 1. The paper has proved the following generalized Golomb conjecture:if GF(q)is a finitc field and a,b,θ,are three nonzero elements,then there are two primitive ...
然后artin 上的证明更强一点，核心思路是知道F上f既约并假定在L上也既约，然后f一定整除构造的h，然...
Pogudin, G.A.: The primitive element theorem for differential fields with zero derivation on the base field. J. Pure Appl. Algebra 219 (9), 4035–4041 (2015) MathSciNet MATHGleb A Pogudin. The primitive element theorem for differential fields with zero derivation on the ground field. ...
We establish a Primitive Element Theorem for fields equipped with several commuting operators such that each of the operators is either a derivation or an automorphism. More precisely, we show that for every extension $F \\subset E$ of such fields of zero characteristic such that $\\bullet$ ...
For an element g∈F its (right) Fox derivatives g x i are uniquely defined by the formula g-1=∑ i=1 n (x i -1)g x i . So, to a system of elements y 1 ,y 2 ,,y k in F there is associated the Jacobi matrix J=J(y 1 ,,y k )=|y i x j | t with n rows and...
Erratum: The primitive element theorem for commutative algebras (Houston Journal of Mathematics) If R T is an extension of (commutative integral) domains, Λ(T/R) is defined as the supremum of the lengths of chains of intermediate fields in the extens... DD Anderson,DE Dobbs,B Mullins - ...
The simultaneousoccurrence of primitive and free elements in F q m is given by the following theorems.Theorem 1.1. (Primitive normal basis theorem). In the f i nite f i eld F q m , there alwaysexists some element which is simultaneously primitive and free.This result was f i rst proved...
By Horie [4, Theorem 2], l [??] [h.sup.-.sub.n]/[h.sup.-.sub.n-1] for all n [greater than or equal to] 1 if l is a primitive root modulo [p.sup.2] and l is larger than an explicit but complicated constant depending on p. A note on the relative class number of the...
Along the proof, weextend a theorem due to White about the Lipschitz metric on outer space totrees in the boundary, showing that the infimal Lipschitz constant of an$F_N$-equivariant map between the metric completion of any two minimal, verysmall $F_N$-trees is equal to the supremal ...
Theorem 1.3 [1, Cheon and Hahn, 1999] LetEbe an elliptic curve defined over a number fieldK. TakePinE(K). Consider the sequence\{B_n(P,O)\}_{n\in \mathbb {Z}}. Suppose thatPis a non-torsion point. Then, for all but finitely manyn\in \mathbb {Z},B_n(P,O)has a primitiv...