Related papers: The Inverse Semigroup Theory of Elementary Arithme…

A recent paper studied an inverse submonoid $M_n$ of the rook monoid, by representing the nonzero elements of $M_n$ via certain triplets belonging to $\mathbb{Z}^3$. In this short note, we allow the triplets to belong to $\mathbb{R}^3$. We…

We consider a generalization of representations of quivers that can be derived from the ordinary representations of quivers by considering a product of arbitrary classical groups instead of a product of the general linear groups and by…

In this paper we study submonoids of the monoid $\mathscr{I}_\infty^{\,\Rsh\!\!\!\nearrow}(\mathbb{N})$ of almost monotone injective co-finite partial selfmaps of positive integers $\mathbb{N}$. Let…

We study the arithmetic of seminormal $v$-noetherian weakly Krull monoids with nontrivial conductor which have finite class group and prime divisors in all classes. These monoids include seminormal orders in holomorphy rings in global…

This report assumes the basics of inverse semigroup theory as described in the first primer but goes on to show how they may be analysed using ideas from category theory.

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…

We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and…

Inverse semigroups are a class of semigroups whose structure induces a compatible partial order. This partial order is examined so as to establish mirror properties between an inverse semigroup and the semilattice of its idempotent…

Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the…

We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations.…

We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated by a Mealy automaton encoding the behaviour of such a…

Multifraction reduction is a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite…

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…

We revisit our construction of the Thompson groups from the polycyclic inverse monoids in the light of new research. Specifically, we prove that the Thompson group $G_{n,1}$ is the group of units of a Boolean inverse monoid $C_{n}$ called…

We propose a way of associating to each finitely generated monoid or semigroup a formal language, called its loop problem. In the case of a group, the loop problem is essentially the same as the word problem in the sense of combinatorial…

In this paper, we consider the inverse submonoids $AM_n$ of monotone transformations and $AO_n$ of order-preserving transformations of the alternating inverse monoid $AI_n$ on a chain with $n$ elements. We compute the cardinalities,…

As part of his study of representations of the polycylic monoids, M.V. Lawson described all the closed inverse submonoids of a polycyclic monoid $P_n$ and classified them up to conjugacy. We show that Lawson's description can be extended to…

The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…

In this thesis we study the subsemigroup structure of the symmetric inverse monoid $I_X$, the inverse semigroup of bijections between subsets of the set $X$, when $X$ is an infinite set. We explore three different approaches to this task.…

The aim of this paper is threefold: a) Finding new direct and inverse results in the additive number theory concerning Minkowski sums of dilates. b) Finding a connection between the above results and some direct and inverse problems in the…