# Generalized Formal Degree

## Related Articles

- Polynomials with small discriminants and regular systems of real algebraic numbers. Bernik, V. I.; Kukso, O. S. // Journal of Mathematical Sciences;Aug2006, Vol. 137 Issue 2, p4612
The distribution of special algebraic numbers is studied, and an optimal regular system is constructed. Bibliography: 11 titles.

- Some Results Connected with the Class Number Problem in Real Quadratic Fields. Grytczuk, Aleksander; Grytczuk, Jarosław // Acta Mathematica Sinica;Oct2005, Vol. 21 Issue 5, p1107
We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h( d) of the real quadratic field $$ \mathbb{Q}{\left( {{\sqrt d }} \right)} $$. In particular, we give a new proof of the result of Hasse,...

- algebraic numbers. // Hutchinson Dictionary of Scientific Biography;2005, p1
In mathematics, numbers that satisfy a polynomial equation with rational coefficients: for example, âˆš2 solves x2 - 2 = 0. Real numbers that are not algebraic are called

trancendental numbers . Although there is an infinity of algebraic numbers, there is... - The embedding problem with non-Abelian kernel for local fields. Ishkhanov, V.; Lur�e, B. // Journal of Mathematical Sciences;Sep2009, Vol. 161 Issue 4, p553
The embedding problem of local fields with p-groups is equivalent to its associated Abelian problem if the inequality d = r + 2 is valid; here d and r are the numbers of generators of the Demushkin group and of the Galois group of an embedded field. Bibliography: 6 titles.

- The cardinal coefficients of the Ideal $${{\mathcal {I}}_{f}}$$. Osuga, Noboru; Kamo, Shizuo // Archive for Mathematical Logic;Nov2008, Vol. 47 Issue 7/8, p653
In 2002, Yorioka introduced the s-ideal $${{\mathcal {I}}_f}$$ for strictly increasing functions f from ? into ? to analyze the cofinality of the strong measure zero ideal. For each f, we study the cardinal coefficients (the additivity, covering number, uniformity and cofinality) of $${{\mathcal...

- HZ-ALGEBRA SPECTRA ARE DIFFERENTIAL GRADED ALGEBRAS. Shipley, Brooke // American Journal of Mathematics;Apr2007, Vol. 129 Issue 2, p351
We show that the homotopy theory of differential graded algebras coincides with the homotopy theory of HZ-algebra spectra. Namely, we construct Quillen equivalences between the Quillen model categories of (unbounded) differential graded algebras and HZ-algebra spectra. We also construct Quillen...

- WHITNEY'S EXTENSION PROBLEMS AND INTERPOLATION OF DATA. Fefferman, Charles // Bulletin (New Series) of the American Mathematical Society;Apr2009, Vol. 46 Issue 2, p207
Given a function f : E â†’ R with E âŠ‚ ℝ:n, we explain how to decide whether f extends to a âŠ‚m function F on â„n. If E is finite, then one can efficiently compute an F as above, whose Cm norm has the least possible order of magnitude (joint work with B. Klartag).

- Transitive parabolic unitals in semifield planes. Johnson, Norman // Journal of Geometry;2006, Vol. 85 Issue 1/2, p61
Every semifield plane with spread in PG(3, K), where K is a field admitting a quadratic extension K +, is shown to admit a transitive parabolic unital.

- On Archimedean Fields. Schleiermacher, Adolf // Journal of Geometry;2009, Vol. 92 Issue 1/2, p143
In this note we consider formally real fields that admit only of Archimedean orderings. Such fields will be called Archimedean. We establish necessary and sufficient conditions for a formally real field to be Archimedean. We also characterize in terms of convexity the positive cones of...