Exchange PF-rings and almost PP-rings.
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.
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 is an analytic curve on an analytic variety and is a formal power series which is convergent when restricted...
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.
Let be a continuous, piecewise-polynomial function. The Pierce-Birkhoff conjecture (1956) is that any such is representable in the form , for some finite collection of polynomials . (A simple example is .) In 1984, L. Mahé and, independently, G. Efroymson, proved this for ; it remains open for . 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;...
Soient un corps valué et est une extension monogène finie de définie par , alors toute valuation de qui prolonge définit une pseudo-valuation de de noyau l’idéal . Nous savons associer à une famille de valuations de , 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 de appartienne à la famille admissible associée à une pseudo-valuation...