## 87 Citations

### Proto-exact categories of modules over semirings and hyperrings

- Mathematics
- 2022

Proto-exact categories, introduced by Dyckerhoff and Kapranov, are a generalization of Quillen exact categories which provide a framework for defining algebraic K-theory and Hall algebras in a…

### Superring of Polynomials over a Hyperring

- MathematicsMathematics
- 2019

A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring…

### From monoids to hyperstructures: in search of an absolute arithmetic

- Mathematics
- 2010

We show that the trace formula interpretation of the explicit formulas expresses the counting functionN.q/ of the hypothetical curveC associated to the Riemann zeta function, as an intersection…

### A Field Theory Problem Relating to Questions in Hyperfield Theory

- Mathematics
- 2011

M. Krasner introduced the notions of the hypefield and the hyperring in 1956. Much later, he constructed the quotient hyperfield/hyperrring, using a field/ring and a subgroup of its multiplicative…

### Realization spaces of matroids over hyperfields

- Mathematics
- 2015

We study realization spaces of matroids over hyperfields (in the sense of Baker and Bowler). More precisely, given a matroid M and a hyperfield H we determine the space of all H-matroids over M. This…

### On the arithmetic of the BC-system

- Mathematics
- 2011

For each prime p and each embedding of the multiplicative group of an algebraic closure of F_p as complex roots of unity, we construct a p-adic indecomposable representation of the integral BC-system…

### Quantales and Hyperstructures

- Mathematics
- 2016

Author(s): Dudzik, Andrew Joseph | Advisor(s): Baker, Matt; Olsson, Martin | Abstract: We present a theory of lattice-enriched semirings, called \emph{quantic semirings}, which generalize both…

### Model Theory of Adeles and Number Theory

- Mathematics
- 2020

This paper is a survey on model theory of adeles and applications to model theory, algebra, and number theory. Sections 1-12 concern model theory of adeles and the results are joint works with Angus…

## References

SHOWING 1-10 OF 73 REFERENCES

### A Realization of Hyperrings

- Mathematics
- 2006

The purpose of this article is to present certain results arising from a study of theory of hyperrings. By a hyperring we mean a Krasner hyperring, that is, a triple (R, +,·) is such that (R, +) is a…

### From monoids to hyperstructures: in search of an absolute arithmetic

- Mathematics
- 2010

We show that the trace formula interpretation of the explicit formulas expresses the counting functionN.q/ of the hypothetical curveC associated to the Riemann zeta function, as an intersection…

### The Weil Proof and the Geometry of the Adèles Class Space

- Mathematics
- 2009

This paper explores analogies between the Weil proof of the Riemann hypothesis for function fields and the geometry of the adeles class space, which is the noncommutative space underlying Connes'…

### Au-dessous de SpecZ .

- Mathematics
- 2009

In this article we use the theories of relative algebraic geometry and of homotopical algebraic geometry (cf. [HAGII]) to construct some categories of schemes defined under Spec ℤ. We define the…

### Schemes over 𝔽1 and zeta functions

- MathematicsCompositio Mathematica
- 2010

Abstract We determine the real counting function N(q) (q∈[1,∞)) for the hypothetical ‘curve’ $C=\overline {\mathrm {Spec}\,\Z }$ over 𝔽1, whose corresponding zeta function is the complete Riemann…

### An Elementary Proof of the Fundamental Theorem of Projective Geometry (Dedicated to Alfred Frölicher)

- Mathematics
- 2002

The following version of the fundamental theorem is proved: Let V, W be vector spaces and g: P(V)\E → P(W) a morphism between the associated projective spaces. If the image of g is not contained in a…

### Characteristic 1 , entropy and the absolute point

- Mathematics
- 1997

We show that the mathematical meaning of working in characteristic one is directly connected to the fields of idempotent analysis and tropical algebraic geometry and we relate this idea to the notion…

### Characteristic one, entropy and the absolute point

- Mathematics
- 2009

We show that the mathematical meaning of working in characteristic one is directly connected to the fields of idempotent analysis and tropical algebraic geometry and we relate this idea to the notion…

### Finite Projective Planes

- Mathematics
- 2006

We propose graph theoretic equivalents for existence of a finite projective plane. We then develop a new approach and see that the problem of existence of a finite projective plane of order n is…