Related papers: Subatomicity in Rank-2 Lattice Monoids

We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…

Subatomic systems were recently introduced to identify the structural principles underpinning the normalization of proofs. "Subatomic" means that we can reformulate logical systems in accordance with two principles. Their atomic formulas…

If $G$ is a semisimple Lie group of real rank at least 2 and $\Gamma$ is an irreducible lattice in $G$, then every homomorphism from $\Gamma$ to the outer automorphism group of a finitely generated free group has finite image.

We will prove bi-interpretability of the arithmetic $\N = \langle N, +,\cdot, 0, 1\rangle$ and the weak second order theory of $\N$ with the free monoid $\mathbb{M}_X$ of finite rank greater than 1 and with a non-trivial partially…

The incompressibility of finite fermionic systems is investigated using analytical approaches and microscopic models. The incompressibility of a system is directly linked to the zero-point kinetic energy of constituent fermions, and this is…

Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group…

We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the…

We prove that if $M$ is a monoid and $A$ a finite set with more than one element, then the residual finiteness of $M$ is equivalent to that of the monoid consisting of all cellular automata over $M$ with alphabet $A$.

We prove that a monoid is sofic, in the sense recently introduced by Ceccherini-Silberstein and Coornaert, whenever the J-class of the identity is a sofic group, and the quotients of this group by orbit stabilisers in the rest of the monoid…

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…

A distributive lattice $L$ with minimum element $0$ is called decomposable if $a$ and $b$ are not comparable elements in $L$ then there exist $\overline{a},\overline{b}\in L$ such that $a=\overline{a}\vee(a\wedge b),…

This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…

For ultracold and Bose-condensed atoms contained in periodic optical potential wells the quantized nature of their motion is clearly visible. The motion of the atomic wavepacket can also be accurately controlled. For those systems the…

Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our…

A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. We show that the 6-element Brandt monoid generates a finitely universal variety of monoids and, by the previous results, it…

Let $S \subset \mathbb{N}_0$ be a numerical monoid and let $\mathcal P_{\mathrm{fin}} (S)$, resp $\mathcal P_{\mathrm{fin},0}(S)$, denote the power monoid, resp. the restricted power monoid, of $S$, that is the set of all finite nonempty…

Arithmetical congruence monoids, which arise in non-unique factorization theory, are multiplicative monoids $M_{a,b}$ consisting of all positive integers $n$ satsfying $n \equiv a \bmod b$. In this paper, we examine the asymptotic behavior…

We study the class of acts with embeddings as an abstract elementary class. We show that the class is always stable and show that superstability in the class is characterized algebraically via weakly noetherian monoids. The study of these…

Let $H$ be a multiplicatively written monoid with identity $1_H$ (in particular, a group). We denote by $\mathcal P_{\rm fin,\times}(H)$ the monoid obtained by endowing the collection of all finite subsets of $H$ containing a unit with the…

In an atomic, cancellative, commutative monoid, the \omega-value measures how far an element is from being prime. In numerical monoids, we show that this invariant exhibits eventual quasilinearity (i.e., periodic linearity). We apply this…