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Extension of semiclean rings

Chahrazade Bakkari, Mohamed Es-Saidi, Najib Mahdou, Moutu Abdou Salam Moutui (2022)

Czechoslovak Mathematical Journal

This paper aims at the study of the notions of periodic, UU and semiclean properties in various context of commutative rings such as trivial ring extensions, amalgamations and pullbacks. The results obtained provide new original classes of rings subject to various ring theoretic properties.

Extension of the Two-Variable Pierce-Birkhoff conjecture to generalized polynomials

Charles N. Delzell (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Let h : ℝ n → ℝ be a continuous, piecewise-polynomial function. The Pierce-Birkhoff conjecture (1956) is that any such h is representable in the form sup i inf j f i j , for some finite collection of polynomials f i j ∈ ℝ [ x 1 , ... , x n ] . (A simple example is h ( x 1 ) = | x 1 | = sup { x 1 , - x 1 } .) In 1984, L. Mahé and, independently, G. Efroymson, proved this for n ≤ 2 ; it remains open for n ≥ 3 . In this paper we prove an analogous result for “generalized polynomials” (also known as signomials), i.e., where the exponents are allowed to be arbitrary real numbers, and not just natural numbers;...

Extensions de valuation et polygone de Newton

Michel Vaquié (2008)

Annales de l’institut Fourier

Soient ( K , ν ) un corps valué et L est une extension monogène finie de K définie par L = K [ x ] / ( P ) , alors toute valuation de L qui prolonge ν définit une pseudo-valuation ζ de K [ x ] de noyau l’idéal ( P ) . Nous savons associer à ζ une famille de valuations de K [ x ] , appelée famille admissible, construite de façon explicite à partir de valuations augmentées et de valuations augmentées limites.Nous donnons une condition nécessaire et suffisante pour qu’une valuation μ de K [ x ] appartienne à la famille admissible associée à une pseudo-valuation...

Extremal functions of the Nevanlinna-Pick problem and Douglas algebras

V. Tolokonnikov (1993)

Studia Mathematica

The Nevanlinna-Pick problem at the zeros of a Blaschke product B having a solution of norm smaller than one is studied. All its extremal solutions are invertible in the Douglas algebra D generated by B. If B is a finite product of sparse Blaschke products (Newman Blaschke products, Frostman Blaschke products) then so are all the extremal solutions. For a Blaschke product B a formula is given for the number C(B) such that if the NP-problem has a solution of norm smaller than C(B) then all its extremal...

Factorial Fermat curves over the rational numbers

Peter Malcolmson, Frank Okoh, Vasuvedan Srinivas (2016)

Colloquium Mathematicae

A polynomial f in the set {Xⁿ+Yⁿ, Xⁿ +Yⁿ-Zⁿ, Xⁿ +Yⁿ+Zⁿ, Xⁿ +Yⁿ-1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.

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