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Existence of Gorenstein projective resolutions and Tate cohomology

Peter Jørgensen (2007)

Journal of the European Mathematical Society

Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.

Exposé on a conjecture of Tougeron

Joseph Becker (1977)

Annales de l'institut Fourier

An algebra homomorphism of the locatized affine rings of an algebraic variety is continuous in the Krull topology of the respective local rings. It is not necessarily open or closed in the Krull topology. However, we show that the induced map on the associated analytic local rings is also open and closed in the Krull topology. To do this we prove a conjecture of Tougeron which states that if η is an analytic curve on an analytic variety V and f is a formal power series which is convergent when restricted...

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 : n 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 [ 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...

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