We show that the theory of hyperrings, due to M. Krasner, supplies a perfect framework to understand the algebraic structure of the adèle class space HK = AK/K of a global field K. After promoting F1 to a hyperfield K, we prove that a hyperring of the form R/G (where R is a ring and G ⊂ R× is a subgroup of its multiplicative group) is a hyperring extension of K if and only if G ∪ {0} is a subfi...

This essay links two strands of Robert O. Keohane’s work. After Hegemony and his essays in International Regimes and Cooperation Under Anarchy relied on microeconomic reasoning to place the international institutions, norms, rules and procedures that we know as regimes at the center of the study of international relations. With Stephen Krasner, Robert Axelrod and others, Keohane defined the fun...

We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. Nonexistence of stable threesome matchings. Mathematical Social Sciences 16, 207–209] showed that not all instances of 3GSM allow stable matchings. Boros et al. [Boros, E., Gurvich, V., Jaslar, S., Krasner, D., 2004. Stable matchings in three-sided systems with cyclic preferences. Discrete Mathematic...

Running title: Insulin and postprandial vascular function Thomas Forst MD; Andreas Pfützner MD, PhD; Frank Flacke PhD; Alan Krasner MD; Cloth Hohberg MD; Eda Tarakci; Philip Pichotta PhD; Senait Forst; Solomon Steiner PhD Corresponding Author: Thomas Forst, MD Email: [email protected] Clinical trial reg. no. NCT00849576; www.clinicaltrials.gov Submitted 3 March 2009 and accepted 16 September 2009...

From Paleolithic cave paintings to Baroque Florence’s Artemisia Gentileschi, scholars have uncovered many cases in which women’s art was credited to their male contemporaries. This reoccurring dynamic communicates a cultural attitude of explicit disbelief in female abilities known as classical sexism. Even today, this trend persists as female artists’ work is continually dismissed as derivative...

In [3], Nathan Bowler and the first author introduced a category of algebraic objects called tracts defined notion (weak strong) matroids over tract. part paper, we summarize clarify connections to other which have previously been used in connection with matroid theory. For example, show that both partial fields hyperfields are fuzzy rings, rings tracts, these relations compatible theories. We ...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...