An algebraic closure of contains a unique of containing all (algebraic) of within . This subextension is called a of . Since a separable extension of a separable extension is again separable, there are no finite separable extensions of , of degree > 1. Saying this another way, is contained...
L. Fukshansky. Search bounds for zeros of polynomials over the algebraic closure of Q. to appear in Rocky Mountain J. Math., arXiv:math.NT/0512132.Search bounds for zeros of polynomials over the algebraic closure of Q - Fukshansky
arXiv:math/0512133v2 [math.NT] 6 Oct 2006SEARCH BOUNDS FOR ZEROS OF POLYNOMIALS OVER THEALGEBRAIC CLOSURE OF QLENNY FUKSHANSKYAbstract. We discuss existence of explicit search bounds for zeros of polyno-mials with coefficients in a number field. Our main result is a theorem aboutthe ...
Because b is a zero of f(x) = x^4-3 \in Q(a)[x] , so [Q(a,b):Q(a)] is at most 4 . [Q(a,b):Q(a)][Q(a):Q] \leq 12 So [Q(\sqrt[3]2, \sqrt[4]3) : Q] = 12 E5 Suppose we know h(x) = 15x^4-10x^2+9x+21 is irreducible over Q . Let \beta be...
Two elliptic curves are isomorphic over ¯¯¯Fq if and only if they both have the same j-invariant, where ¯¯¯Fq denotes the algebraic closure of 𝔽q. Moreover, given an element j0 of 𝔽q, there exists an elliptic curve over 𝔽q with j-invariant equal to j0. The ...
We begin by writing the equation of E in its canonical form over the algebraic closure of GF(q): X22X3-X1(X1-X3)(X1-ωX3)=0 with ω≠0,1. If Q is an affine point, say Q(x,y,1), the change of the projective frame X1=X1′+xX2′,X2=yX2′+X3′,X3=X2′takes Q to ...
Integral closure14Q0513P10Let $${\\fancyscript{C}}$$ be an irreducible...doi:10.1007/s11786-014-0193-xM'hammed El KahouiDepartment of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakech, MoroccoZakari Yaou Moussa...
In particular, (in the former case) by a vertex, edge, rhombus in Q we mean, respectively (the closure of) a 0-, 1-, 2-dimensional cell of this complex, and (in the latter case) when writing [Math Processing Error]ζ∈Q, we mean that [Math Processing Error]ζ is a cube of Q...
The Zariski closure of the orbit[Math Processing Error]Xπ¯:=B_πB+¯⊆CN×Nis calledthe matrix Schubert varietyof[Math Processing Error]π. Rothe presented a combinatorial technique for visualizing inversions of the permutation[Math Processing Error]π. ...
Small zeros of quadratic forms over the algebraic closure of QQuadratic formsbilinear formsheightsLet N u2265 2 be an integer, F a quadratic form in N variables over $overline{mathbb{Q}}$, and $Z subseteq overline{mathbb{Q}}^N$ an L-dimensional subspace, 1 u2264 L u2264 N. We ...