In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing...

Look up ramification in Wiktionary, the free dictionary. Ramification may refer to: Ramification (mathematics), a geometric term used for 'branching out'...

from earlier resolutions of ramification as problematic for their own algorithms. Non-monotonic logic Ramification (mathematics) Nikos Papadakis "Actions...

information on the ramification phenomena of the extension. In mathematics, the ramification theory of valuations studies the set of extensions of a valuation...

{\displaystyle \Omega _{X/Y}} is zero. Finite extensions of local fields Ramification (mathematics) Hartshorne 1977, Ch. IV, § 2. Grothendieck & Dieudonné 1967,...

Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer...

In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

Dirichlet's unit theorem Discriminant of an algebraic number field Ramification (mathematics) Root of unity Gaussian period Fermat's Last Theorem Class number...

by Emmy Noether (perhaps known earlier?). What matters here is tame ramification. In terms of the discriminant D of L, and taking still K = Q, no prime...

restriction of w to K is v. The set of all such extensions is studied in the ramification theory of valuations. Let L/K be a finite extension and let w be an extension...

f(z_{0})} is a positive integer called the ramification index of z 0 {\displaystyle z_{0}} . If the ramification index is greater than 1, then z 0 {\displaystyle...

The set of exceptional points on W {\displaystyle W} is called the ramification locus (i.e. this is the complement of the largest possible open set W...

group is abelian). The 2-torus double-covers the 2-sphere, with four ramification points. Every conformal structure on the 2-torus can be represented as...

Theory and Its Ramifications Journal of Logic and Analysis Journal of Mathematical Biology Journal of Mathematical Logic Journal of Mathematical Physics Journal...

when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It is a prototype result for many...

proved by Cahit Arf. The theorem deals with the upper numbered higher ramification groups of a finite abelian extension L / K {\displaystyle L/K} . So assume...

In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field...

ramification of prime ideals when lifted to an extension field, a basic problem of algebraic number theory, bears some resemblance with ramification in...

In algebraic number theory, through completion, the study of ramification of a prime ideal can often be reduced to the case of local fields where a more...

A prototypical example is intuitionistic type theory, which retains ramification (without the explicit levels) so as to discard impredicativity. The 'levels'...

lies a single ramification point P α {\displaystyle P_{\alpha }} with corresponding different exponent (not to confused with the ramification index) equal...

is three positive integers a, b, c such that a2 + b2 = c2. ramification The ramification theory. relatively prime See coprime. ring of integers The ring...

41403 Ogg, A. P. (1967), "Elliptic curves and wild ramification", American Journal of Mathematics, 89 (1): 1–21, doi:10.2307/2373092, ISSN 0002-9327,...

number field K, with respect to the field trace. It then encodes the ramification data for prime ideals of the ring of integers. It was introduced by Richard...

when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It is a prototype result for many...

is the ramification index e ( P α , i ) {\displaystyle e(P_{\alpha ,i})} at each of the ( m , r α ) {\displaystyle (m,r_{\alpha })} ramification points...

In mathematics, a tangle is generally one of two related concepts: In John Conway's definition, an n-tangle is a proper embedding of the disjoint union...

ISSN 0020-9910. S2CID 8937648. Calegari, Frank; Emerton, Matthew (2005). "On the ramification of Hecke algebras at Eisenstein primes". Inventiones Mathematicae. 160...

In mathematics, racks and quandles are sets with binary operations satisfying axioms analogous to the Reidemeister moves used to manipulate knot diagrams...