Related papers: Generalizations of free monoids

We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the…

Let H be an algebraic group scheme over a field k acting on a commutative k-algebra A which is a unique factorisation domain. We show that, under certain mild assumptions, the monoid of nonzero H-stable principal ideals in A is free…

We first study commutative, pointed monoids providing basic definitions and results in a manner similar commutative ring theory. Included are results on chain conditions, primary decomposition as well as normalization for a special class of…

The divisorial gonality of a graph is the minimum degree of a positive rank divisor on that graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration to divisors that place at most \(1\) chip on each…

We define and explore semireflection monoids on a finite-dimensional vector space. These are monoids generated by semireflections: linear maps fixing a subspace of codimension 1. We mostly focus on the case of projection monoids (where the…

In this article we describe the $G\times G$-equivariant $K$-ring of $X$, where $X$ is a regular compactification of a connected complex reductive algebraic group $G$. Furthermore, in the case when $G$ is a semisimple group of adjoint type,…

We extend the classical notion of standardly stratified $k$-algebra (stated for finite dimensional $k$-algebras) to the more general class of rings, possibly without $1,$ with enough idempotents. We show that many of the fundamental…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

We define a notion of $\infty$-properads that generalises $\infty$-operads by allowing operations with multiple outputs. Specializing to the case where each operation has a single output provides a simple new perspective on…

In this paper we give a new generalization of token graphs. Given two integers $1\leq m \leq k$ and a graph $G$ we define the generalized token graph of the graph $G$, to be the graph $F_k^m(G)$ whose vertices correspond to configurations…

Categorical models of the exponential modality of linear logic will often, but not always, support an operation of differentiation. When they do, we speak of a monoidal differential modality; when they do not, we have merely a monoidal…

We classify all the simple modules for the algebra of relations on a finite set, give their dimension, and find the dimension of the Jacobson radical of the algebra.

We prove several results concerning finitely generated submonoids of the free monoid. These results generalize those known for free submonoids. We prove in particular that if $X=Y\circ Z$ is a composition of finite sets of words with $Y$…

In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.

Let $K_d$ be the complete metric graph on $d$ vertices. We compute the gonality of graphs obtained from $K_d$ by omitting edges forming a $K_h$, or general configurations of at most $d-2$ edges. We also investigate if these graphs can be…

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…

We introduce a general construction on 2-monads. We develop background on maps of 2-monads, their left semi-algebras, and colimits in 2-category. Then, we introduce the construction of a colimit induced by a map of 2-monads, show that we…

We introduce an embedding of the free magma on a set A into the direct product of the free magma on a singleton set and the free semigroup on A. This embedding is then used to prove several theorems related to algebraic independence of…

We introduce and study blob and framed blob monoids. In particular, several realizations of these monoids are given. We compute the cardinality of the framed blob monoid and derive some combinatorial formulas involving this cardinality.

In this paper we identify different classes of free group extension using core graphs. We show that every free group extension $H\leq K\leq F$ has a base $B$ such that the associated pointed graph morphism…