相关论文: Supertropical Monoids II: Lifts, Transmissions, an…

Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of…

Within a subclass of monoids (with zero) a structural characterization is given of those that are associated to topologically transitive subshifts with Property (A).

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of $A$, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity…

In 2010, Izhakian & Margolis proved that the bicyclic monoid admits a representation as a semigroup of upper triangular tropical matrices. We extend this result by classifying all one-relation monoids which admit such representations. We…

The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…

We introduce and investigate the category of factorization of a multiplicative, commutative, cancellative, pre-ordered monoid $A$, which we denote $\mathcal{F}(A)$. The objects of $\mathcal{F}(A)$ are factorizations of elements of $A$, and…

This article reviews the non-perturbative structure of certain higher derivative terms in the type II string theory effective action and their connection to one-loop effects in eleven-dimensional supergravity compactified on a torus. New…

Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…

This paper is written as a brief introduction for beginning graduate students. The picture of electron waves moving in a cristalline potential and interacting weakly with each other and with cristalline vibrations suffices to explain the…

We construct algebraic cobordism spectra MSL and MSp. They are commutative monoids in the category of symmetric T^{2}- spectra. The spectrum MSp comes with a natural symplectic orientation given either by a tautological Thom class th^{MSp}…

We prove that commutative semirings in a cartesian closed presentable $\infty$-category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product-preserving functors from the $(2,1)$-category of bispans of finite sets. In other…

We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…

This is the first part of a series of three strongly related papers in which three equivalent structures are studied: - internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans -…

We relate the old and new cohomology monoids of an arbitrary monoid $M$ with coefficients in semimodules over $M$, introduced in the author's previous papers, to monoid and group extensions. More precisely, the old and new second cohomology…

We prove that, for any $n$, the monoid of all $n \times n$ supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities. These identities are carried over to walks on labeled-weighted digraphs with double…

The tropical semifield, i.e., the real numbers enhanced by the operations of addition and maximum, serves as a base of tropical mathematics. Addition is an abelian group operation, whereas the maximum defines an idempotent semigroup…

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…

In the literature, one finds several competing notions for the super (i.e., Z/2-graded) analog of a monoidal category. The goal of this paper is to clarify these definitions and the connections between them. We also discuss in detail the…

The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max, +),…

A semiring generalises the notion of a ring, replacing the additive abelian group structure with that of a commutative monoid. In this paper, we study a notion positioned between a ring and a semiring -- a semiring whose additive monoid is…