81 research outputs found

    Finitely generated abelian groups of units

    Get PDF
    In 1960 Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In this paper we address Fuchs' question for {\it finitely generated abelian} groups and we consider the problem of characterizing those groups which arise in some fixed classes of rings C\mathcal C, namely the integral domains, the torsion free rings and the reduced rings. To determine the realizable groups we have to establish what finite abelian groups TT (up to isomorphism) occur as torsion subgroup of A∗A^* when AA varies in C\mathcal C, and on the other hand, we have to determine what are the possible values of the rank of A∗A^* when (A∗)tors≅T(A^*)_{tors}\cong T. Most of the paper is devoted to the study of the class of torsion-free rings, which needs a substantially deeper study.Comment: 28 page

    Upper ramification jumps in abelian extensions of exponent p

    Full text link
    In this paper we present a classification of the possible upper ramification jumps for an elementary abelian p-extension of a p-adic field. The fundamental step for the proof of the main result is the computation of the ramification filtration for the maximal elementary abelian p-extension of the base field K. This is a generalization of a previous work of the second author and Dvornicich where the same result is proved under the assumption that K contains a primitive p-th root of unity. Using the class field theory and the explicit relations between the normic group of an extension and its ramification jumps, it is fairly simple to recover necessary and sufficient conditions for the upper ramification jumps of an elementary abelian p-extension of K.Comment: 9 page

    On Fuchs' Problem about the group of units of a ring

    Get PDF
    In cite[Problem 72]{Fuchs60} Fuchs posed the problem of characterizing the groups which are the groups of units of commutative rings. In the following years, some partial answers have been given to this question in particular cases. In a previous paper cite{DDcharp} we dealt with finite characteristic rings. In this paper we consider Fuchs' question for finite groups and we address this problem in two cases. Firstly, we study the case of torson-free rings and we obtain a complete classification of the finite groups of units which arise in this case. Secondly, we examine the case of characteristic zero rings obtaining, a pretty good description of the possible groups of units equipped with families examples of both realizable and non-realizable groups. The main tools to deal with this general case are the Pearson and Schneider splitting of a ring cite{PearsonSchneider70}, our previous results on finite characteristic rings cite{DDcharp} and our classification of the groups of units of torsion-free rings. As a consequence of our results we completely answer Ditor's question cite{ditor} on the possible cardinalities of the group of units of a ring

    An equivalence between local fields

    Get PDF
    AbstractThe p-component of the index of a number field K depends only on the completions of K at the primes over p. In this paper we define an equivalence relation between m-tuples of local fields such that, if two number fields K and K′ have equivalent m-tuples of completions at the primes over p, then they have the same p-component of the index. This equivalence can be interpreted in terms of the decomposition groups of the primes over p of the normal closures of K and K′

    In Search for Multi-Target Ligands as Potential Agents for Diabetes Mellitus and Its Complications - A Structure-Activity Relationship Study on Inhibitors of Aldose Reductase and Protein Tyrosine Phosphatase 1B

    Get PDF
    Diabetes mellitus (DM) is a complex disease which currently affects more than 460 million people and is one of the leading cause of death worldwide. Its development implies numerous metabolic dysfunctions and the onset of hyperglycaemia-induced chronic complications. Multiple ligands can be rationally designed for the treatment of multifactorial diseases, such as DM, with the precise aim of simultaneously controlling multiple pathogenic mechanisms related to the disease and providing a more effective and safer therapeutic treatment compared to combinations of selective drugs. Starting from our previous findings that highlighted the possibility to target both aldose reductase (AR) and protein tyrosine phosphatase 1B (PTP1B), two enzymes strictly implicated in the development of DM and its complications, we synthesised 3-(5-arylidene-4-oxothiazolidin-3-yl)propanoic acids and analogous 2-butenoic acid derivatives, with the aim of balancing the effectiveness of dual AR/PTP1B inhibitors which we had identified as designed multiple ligands (DMLs). Out of the tested compounds, 4f exhibited well-balanced AR/PTP1B inhibitory effects at low micromolar concentrations, along with interesting insulin-sensitizing activity in murine C2C12 cell cultures. The SARs here highlighted along with their rationalization by in silico docking experiments into both target enzymes provide further insights into this class of inhibitors for their development as potential DML antidiabetic candidates

    The Solar Particle Acceleration Radiation and Kinetics (SPARK) Mission Concept

    Get PDF
    © 2023by the authors. Licensee MDPI, Basel, Switzerland. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/Particle acceleration is a fundamental process arising in many astrophysical objects, including active galactic nuclei, black holes, neutron stars, gamma-ray bursts, accretion disks, solar and stellar coronae, and planetary magnetospheres. Its ubiquity means energetic particles permeate the Universe and influence the conditions for the emergence and continuation of life. In our solar system, the Sun is the most energetic particle accelerator, and its proximity makes it a unique laboratory in which to explore astrophysical particle acceleration. However, despite its importance, the physics underlying solar particle acceleration remain poorly understood. The SPARK mission will reveal new discoveries about particle acceleration through a uniquely powerful and complete combination of γ-ray, X-ray, and EUV imaging and spectroscopy at high spectral, spatial, and temporal resolutions. SPARK’s instruments will provide a step change in observational capability, enabling fundamental breakthroughs in our understanding of solar particle acceleration and the phenomena associated with it, such as the evolution of solar eruptive events. By providing essential diagnostics of the processes that drive the onset and evolution of solar flares and coronal mass ejections, SPARK will elucidate the underlying physics of space weather events that can damage satellites and power grids, disrupt telecommunications and GPS navigation, and endanger astronauts in space. The prediction of such events and the mitigation of their potential impacts are crucial in protecting our terrestrial and space-based infrastructure.Peer reviewe

    Serum Albumin Is Inversely Associated With Portal Vein Thrombosis in Cirrhosis

    Get PDF
    We analyzed whether serum albumin is independently associated with portal vein thrombosis (PVT) in liver cirrhosis (LC) and if a biologic plausibility exists. This study was divided into three parts. In part 1 (retrospective analysis), 753 consecutive patients with LC with ultrasound-detected PVT were retrospectively analyzed. In part 2, 112 patients with LC and 56 matched controls were entered in the cross-sectional study. In part 3, 5 patients with cirrhosis were entered in the in vivo study and 4 healthy subjects (HSs) were entered in the in vitro study to explore if albumin may affect platelet activation by modulating oxidative stress. In the 753 patients with LC, the prevalence of PVT was 16.7%; logistic analysis showed that only age (odds ratio [OR], 1.024; P = 0.012) and serum albumin (OR, -0.422; P = 0.0001) significantly predicted patients with PVT. Analyzing the 112 patients with LC and controls, soluble clusters of differentiation (CD)40-ligand (P = 0.0238), soluble Nox2-derived peptide (sNox2-dp; P < 0.0001), and urinary excretion of isoprostanes (P = 0.0078) were higher in patients with LC. In LC, albumin was correlated with sCD4OL (Spearman's rank correlation coefficient [r(s)], -0.33; P < 0.001), sNox2-dp (r(s), -0.57; P < 0.0001), and urinary excretion of isoprostanes (r(s), -0.48; P < 0.0001) levels. The in vivo study showed a progressive decrease in platelet aggregation, sNox2-dp, and urinary 8-iso prostaglandin F2 alpha-III formation 2 hours and 3 days after albumin infusion. Finally, platelet aggregation, sNox2-dp, and isoprostane formation significantly decreased in platelets from HSs incubated with scalar concentrations of albumin. Conclusion: Low serum albumin in LC is associated with PVT, suggesting that albumin could be a modulator of the hemostatic system through interference with mechanisms regulating platelet activation

    The Solar Particle Acceleration Radiation and Kinetics (SPARK) mission concept

    Get PDF
    Particle acceleration is a fundamental process arising in many astrophysical objects, including active galactic nuclei, black holes, neutron stars, gamma-ray bursts, accretion disks, solar and stellar coronae, and planetary magnetospheres. Its ubiquity means energetic particles permeate the Universe and influence the conditions for the emergence and continuation of life. In our solar system, the Sun is the most energetic particle accelerator, and its proximity makes it a unique laboratory in which to explore astrophysical particle acceleration. However, despite its importance, the physics underlying solar particle acceleration remain poorly understood. The SPARK mission will reveal new discoveries about particle acceleration through a uniquely powerful and complete combination of γ-ray, X-ray, and EUV imaging and spectroscopy at high spectral, spatial, and temporal resolutions. SPARK’s instruments will provide a step change in observational capability, enabling fundamental breakthroughs in our understanding of solar particle acceleration and the phenomena associated with it, such as the evolution of solar eruptive events. By providing essential diagnostics of the processes that drive the onset and evolution of solar flares and coronal mass ejections, SPARK will elucidate the underlying physics of space weather events that can damage satellites and power grids, disrupt telecommunications and GPS navigation, and endanger astronauts in space. The prediction of such events and the mitigation of their potential impacts are crucial in protecting our terrestrial and space-based infrastructure
    • …
    corecore