Results 1  10
of
136
Local monomialization of transcendental extensions
"... Suppose that R ⊂ S are local domains such that S dominates R. We will say that R ⊂ S is monomial if R and S are regular and there are regular system of parameters (x1,..., xm) in R and (y1,..., yn) in S, there are units δ1,..., δm in S and an m ×n matrix A of natural numbers such that A has maximal ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Suppose that R ⊂ S are local domains such that S dominates R. We will say that R ⊂ S is monomial if R and S are regular and there are regular system of parameters (x1,..., xm) in R and (y1,..., yn) in S, there are units δ1,..., δm in S and an m ×n matrix A of natural numbers such that A has maximal rank m and
Computation in Real Closed Infinitesimal and Transcendental Extensions of the Rationals
"... Abstract. Recent applications of decision procedures for nonlinear real arithmetic (the theory of real closed fields, or RCF) have presented a need for reasoning not only with polynomials but also with transcendental constants and infinitesimals. In full generality, the algebraic setting for this re ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
for this reasoning consists of real closed transcendental and infinitesimal extensions of the rational numbers. We present a library for computing over these extensions. This library contains many contributions, including a novel combination of Thom’s Lemma and interval arithmetic for representing roots
© Hindawi Publishing Corp. GRADED TRANSCENDENTAL EXTENSIONS OF GRADED FIELDS
, 2002
"... We study transcendency properties for graded field extension and give an application to valued field extensions. 2000 Mathematics Subject Classification: 12F20, 16W50. 1. Introduction. An ..."
Abstract
 Add to MetaCart
We study transcendency properties for graded field extension and give an application to valued field extensions. 2000 Mathematics Subject Classification: 12F20, 16W50. 1. Introduction. An
On the Hasse Principle for the Brauer group of a
"... purely transcendental extension field in one variable over an arbitrary field ..."
Abstract
 Add to MetaCart
purely transcendental extension field in one variable over an arbitrary field
Conservation of the noetherianity by perfect transcendental field extensions
 Rev. Mat. Iberoamericana
"... Let k be a perfect field of characteristic p> 0, k(t)per the perfect closure of k(t) and A a kalgebra. We characterize whether the ring A ⊗k k(t)per = ⋃ m≥0 (A ⊗k k(t 1 p m)) is noetherian or not. As a consequence, we prove that the ring A ⊗k k(t)per is noetherian when A is the ring of formal po ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Let k be a perfect field of characteristic p> 0, k(t)per the perfect closure of k(t) and A a kalgebra. We characterize whether the ring A ⊗k k(t)per = ⋃ m≥0 (A ⊗k k(t 1 p m)) is noetherian or not. As a consequence, we prove that the ring A ⊗k k(t)per is noetherian when A is the ring of formal power series in n indeterminates over k.
NUMBERS: RATIONAL, IRRATIONAL OR TRANSCENDENTAL?
, 2010
"... We talk of rational numbers, irrational numbers, algebraic numbers, transcendental numbers and briefly describe some real numbers π, Euler’s number e, Euler’s Constant γ, Liouville constant α. The first two numbers π and Euler’s number e are used extensively in undergraduate courses, in fact π is kn ..."
Abstract
 Add to MetaCart
We talk of rational numbers, irrational numbers, algebraic numbers, transcendental numbers and briefly describe some real numbers π, Euler’s number e, Euler’s Constant γ, Liouville constant α. The first two numbers π and Euler’s number e are used extensively in undergraduate courses, in fact π
FullDiversity, HighRate SpaceTime Block Codes from Division Algebras
 IEEE TRANS. INFORM. THEORY
, 2003
"... We present some general techniques for constructing fullrank, minimaldelay, rate at least one spacetime block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algeb ..."
Abstract

Cited by 177 (55 self)
 Add to MetaCart
one appropriate for any number of transmit antennas. We study the coding gain and capacity of these codes. Using transcendental extensions we construct arbitrary rate codes that are full rank for arbitrary number of antennas. We also present a method of constructing STBCs using noncyclotomic field
WZ Algorithms for Integrals of Transcendental and Algebraic Extensions of Hypergeometric Kernels
"... . The WZ algorithms for proving hypergeometric multisum/integral identities are extended to more general integrands. Classification Numbers 33c90 In Parnes and Ekhad (1992) there is a WZstyle proof of the generating function for the Jacobi polynomials, P ff;fi n , which is equivalent to the integr ..."
Abstract
 Add to MetaCart
to the integral identity P (ff;fi) n (x) = Z jtj=ffl 2 (ff+fi)dt ae(1 + t + ae) fi (1 \Gamma t + ae) ff t n+1 ; (0:1) where ae = (1 \Gamma 2xt + t 2 ) 1=2 : It seemed likely that this was an example for a more general WZalgorithm for sums and integrals involving algebraic extensions
TRANSCENDENTAL VALUES OF CLASS GROUP LFunctions, II
, 2012
"... Let K be an imaginary quadratic field and f an integral ideal. Denote by Cl(f) the ray class group of f. For every nontrivial character χ of Cl(f), we show that L(1,χ)/π is transcendental. If f = f, then complex conjugation acts on the character group of Cl(f). Denoting by Ĉl(f)+ the orbits of the ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
of the group of characters, we show that the values L(1,χ)asχ ranges over elements of Ĉl(f)+ are linearly independent over Q. We give applications of this result to the study of transcendental values of Petersson inner products and certain special values of Artin Lseries attached to dihedral extensions.
Results 1  10
of
136