Related papers: The ring of fluxions
Green and Tao famously proved in a 2008 paper that there are arithmetic progressions of prime numbers of arbitrary lengths. Soon after, analogous statements were proved by Tao for the ring of Gaussian integers and by L\^e for the polynomial…
This text tries to give an elementary introduction to the mathematical properties of infinite sets. The aim is to keep the approach as simple as possible. Advanced knowledge of mathematics is not necessary for a proper understanding, and…
The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining…
An LR-structure is a tetravalent vertex-transitive graph together with a special type of a decomposition of its edge-set into cycles. LR-structures were introduced in a paper by P. Poto\v{c}nik and S. Wilson, titled `Linking rings…
Originally studied by Conway and Coxeter, friezes appeared in various recreational mathematics publications in the 1970s. More recently, in 2015, Baur, Parsons, and Tschabold constructed periodic infinite friezes and related them to…
The Magnus expansion, introduced by Wilhelm Magnus in 1954, is an infinite Lie series employed to express solutions for first-order homogeneous linear differential equations involving a linear operator. Since its discovery it has evolved…
The first author constructed a $q$-parameterized spherical category $\sC$ over $\mathbb{C}(q)$ in [Liu15], whose simple objects are labelled by all Young diagrams. In this paper, we compute closed-form expressions for the fusion rule of…
We provide new characterizations of pseudo-Frobenius and quasi-Frobenius rings in terms of tight modules. In the process, we also provide fresh perspectives on FGF and CF conjectures. In particular, we propose new natural extensions of…
With a small suitable modification, dropping the projectivity condition, we extend the notion of a Frobenius algebra to grant that a Frobenius algebra over a Frobenius commutative ring is itself a Frobenius ring. The modification introduced…
In \cite{GCF} it is proved that any quadratic irrational number has a representation as a continuous, infinite and periodic fraction. In 1848, Charles Hermite through a letter Jacobi \cite{Per} wondered if this fact could be generalized to…
The ring of Fermat reals is an extension of the real field containing nilpotent infinitesimals, and represents an alternative to Synthetic Differential Geometry in classical logic. In the present paper, our first aim is to study this ring…
In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a sum, product and quotient of some series of positive rational…
We give a new argument for the characterization of the cohomology rings of closed 3-manifolds with coefficients $\mathbb{F}_2$, first given by M. M. Postnikov (in terms of intersection rings) in 1948
In the 1940's Graham Higman initiated the study of finite subgroups of the unit group of an integral group ring. Since then many fascinating aspects of this structure have been discovered. Major questions such as the Isomorphism Problem and…
Cluster algebras were introduced by S. Fomin and A. Zelevinsky in math.RT/0104151; their study continued in math.RA/0208229, math.RT/0305434. This is a family of commutative rings designed to serve as an algebraic framework for the theory…
A Sturmian sequence is an infinite nonperiodic string over two letters with minimal subword complexity. In two papers, the first written by Morse and Hedlund in 1940 and the second by Coven and Hedlund in 1973, a surprising correspondence…
This book is a rigorous and conceptually oriented introduction to ring theory. The emphasis is on structural understanding rather than encyclopedic coverage: rings are studied through ideals, homomorphisms, quotients, and universal…
A quasi-order is a binary, reflexive and transitive relation. In the Journal of Pure and Applied Algebra 45 (1987), S.M. Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered…
We extend the theory of Mackey 2-functors introduced in arXiv:1808.04902 by defining the appropriate notion of rings, namely Green 2-functors. After providing the first results of our theory and abundant examples, we show how all classical…
The starting point of this paper are the Mittag-Leffler polynomials introduced by H. Bateman [1]. Based on generalized integer powers of real numbers and deformed exponential function, we introduce deformed Mittag-Leffler polynomials…