Related papers: Coherency for monoids and purity for their acts

For a semigroup $S$, the covering number of $S$ with respect to semigroups, $\sigma_s(S)$, is the minimum number of proper subsemigroups of $S$ whose union is $S$. This article investigates covering numbers of semigroups and analogously…

Let $R$ be a ring and $M$ be a right $R$-module. $M$ is called neat-flat if any short exact sequence of the form $0\to K\to N\to M\to 0$ is neat-exact i.e. any homomorphism from a simple right $R$-module $S$ to $M$ can be lifted to $N$. We…

Let $X$ be a monoid scheme. We will show that the stalk at any point of $X$ defines a point of the topos $\Qc(X)$ of quasi-coherent sheaves over $X$. As it turns out, every topos point of $\Qc(X)$ is of this form if $X$ satisfies some…

We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In this situation, coherence is equivalent to saying that solution…

For a topological monoid S the dual inverse monoid is the topological monoid of all identity preserving homomorphisms from S to the circle with attached zero. A topological monoid S is defined to be reflexive if the canonical homomorphism…

In a colouring of $\mathbb{R}^d$ a pair $(S,s_0)$ with $S\subseteq \mathbb{R}^d$ and with $s_0\in S$ is \emph{almost monochromatic} if $S\setminus \{s_0\}$ is monochromatic but $S$ is not. We consider questions about finding almost…

A smallish monoid M is a monoid that has a unique 0-minimal ideal I(M) that is a 0-simple subsemigroup and such that its regular J -classes are the group of units and the two in I(M). We show constructively how to embed an arbitrary finite…

This exposition presents recent developments on proper actions, highlighting their connections to representation theory. It begins with geometric aspects, including criteria for the properness of homogeneous spaces in the setting of…

We explore several variations of the notion of purity for the action of Frobenius on schemes defined over finite fields. In particular, we study how these notions are preserved under certain natural operations like quotients for principal…

We present a construction of skew monoidal structures from strong actions. We prove that the existence of a certain adjoint allows one to equip the actegory with a skew monoidal structure and that this adjunction becomes monoidal. This…

In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We show that if a group with a positive presentation has a complete rewriting system $\Re$ that satisfies the condition that each rule in…

For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition.…

A set-theoretical solution of the pentagon equation on a non-empty set $X$ is a function $s:X\times X\to X\times X$ satisfying the relation $s_{23}\, s_{13}\, s_{12}=s_{12}\, s_{23}$, with $s_{12}=s\times \,id_X$, $s_{23}=id_X \times \, s$…

We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is…

We discuss a general framework of monotone skew-product semiflows under a connected group action. In a prior work, a compact connected group $G$-action has been considered on a strongly monotone skew-product semiflow. Here we relax the…

We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ru\v{s}kuc (2024) gave the first example of a finitely presented SIM whose submonoid of right units does…

It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class…

A semigroup $X$ is $absolutely$ (resp. $injectively$) $T_1S$-$closed$ if for any (injective) homomorphism $h:X\to Y$ to a $T_1$ topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. We prove that a commutative semigroup…

Let $S$ be a nonnegative semiring of the real line, called here a positive semiring. We study factorizations in both the additive monoid $(S,+)$ and the multiplicative monoid $(S\setminus\{0\}, \cdot)$. In particular, we investigate when,…

The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.