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Displaying 321 – 340 of 389

On the polynomial-like behaviour of certain algebraic functions

Charles Feffermann, Raghavan Narasimhan (1994)

Annales de l'institut Fourier

Given integers $D > 0, n > 1, 0 < r < n$ and a constant $C > 0$ , consider the space of $r$ -tuples $\vec{P} = (P_{1} ... P_{r})$ of real polynomials in $n$ variables of degree $\leq D$ , whose coefficients are $\leq C$ in absolute value, and satisfying $\det {(\frac{\partial P_{i}}{\partial x_{i}} (0))}_{1 \leq i, j \leq r} = 1$ . We study the family ${f | V}$ of algebraic functions, where $f$ is a polynomial, and $V = {| x | \leq δ, \vec{P} (x) = 0}, δ > 0$ being a constant depending only on $n, D, C$ . The main result is a quantitative extension theorem for these functions which is uniform in $\vec{P}$ . This is used to prove Bernstein-type inequalities which are again uniform with respect to $\vec{P}$ .The proof is based on...

On the Prime Ideal of an Ordering of Higher Level.

Thomas C. Craven (1982)

Mathematische Zeitschrift

On the product of a module by an ideal

A. G. Naoum (1988)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

On the Pythagoras number of a real irreducible algebroid curve.

Jesus J. Ortega (1991)

Mathematische Annalen

On the Radius and the Relation Between the Total Graph of a Commutative Ring and Its Extensions

Zoran Pucanović, Zoran Petrović (2011)

Publications de l'Institut Mathématique

On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.

Harris Hancock (1900)

Journal für die reine und angewandte Mathematik

On the regularity and defect sequence of monomial and binomial ideals

Keivan Borna, Abolfazl Mohajer (2019)

Czechoslovak Mathematical Journal

When $S$ is a polynomial ring or more generally a standard graded algebra over a field $K$ , with homogeneous maximal ideal $𝔪$ , it is known that for an ideal $I$ of $S$ , the regularity of powers of $I$ becomes eventually a linear function, i.e., $reg (I^{m}) = d m + e$ for $m ≫ 0$ and some integers $d$ , $e$ . This motivates writing $reg (I^{m}) = d m + e_{m}$ for every $m \geq 0$ . The sequence $e_{m}$ , called the defect sequence of the ideal $I$ , is the subject of much research and its nature is still widely unexplored. We know that $e_{m}$ is eventually constant. In this article, after...

On the Regularity of Graded k-Algebras of Krull Dimension ...1.

Rickard Sjögren (1992)

Mathematica Scandinavica

On the ring of constants for derivations of power series rings in two variables

Leonid Makar-Limanov, Andrzej Nowicki (2001)

Colloquium Mathematicae

Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].

On the ring of invariants of F*2n.

H.E.A. Campbell, I. Hughes (1991)

Commentarii mathematici Helvetici

On the ring of quotients of a noetherian commutative ring with respect to the Dickson topology

Alberto Facchini (1980)

Rendiconti del Seminario Matematico della Università di Padova

On the ring of the variety of algebras over a ring

Pavol Zlatoš (1983)

Commentationes Mathematicae Universitatis Carolinae

On the rings of formal solutions of polynomial differential equations

Maria-Angeles Zurro (1998)

Banach Center Publications

The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.

On the S-Euclidean minimum of an ideal class

Kevin J. McGown (2015)

Acta Arithmetica

We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses ideas from...

On the singularities of Polar curves.

Eduardo Casas (1983)

Manuscripta mathematica

On the stable equivalence problem for k[x,y]

Robert Dryło (2011)