Related papers: $F$-birestriction monoids in enriched signature

Let $(X,\bullet )$ be a groupoid (binary algebra) and $Bin(X\dot{)}$ denote the collection of all groupoids defined on $X$. We introduce two methods of factorization for this binary system under the binary groupoid product \textquotedblleft…

Let $A$ be a regular ring containing a field of characteristic $p>0$ and let $R=A[x_1,\ldots,x_m,y_1,\ldots,y_n]$ be standard bigraded over $A$, i.e., $\operatorname{bideg}(A)=(0,0)$, $\operatorname{bideg}(x_i)=(1,0)$ and…

A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word problem for…

This article concerns Ehresmann structures in the partition monoid $P_X$. Since $P_X$ contains the symmetric and dual symmetric inverse monoids on the same base set $X$, it naturally contains the semilattices of idempotents of both…

Let $S$ be a semigroup, let $n\in\mathbb{N}$ be a positive natural number, let $A,B\subseteq S$, let $\mathcal{U},\mathcal{V}\in\beta S$ and let let $\mathcal{F}\subseteq\{f:S^{n}\rightarrow S\}$. We say that $A$ is $\mathcal{F}$-finitely…

Let R=S/I be a monomial ring whose minimal free resolution F is rooted. We describe an A-infinity algebra structure on F. Using this structure, we show that R is Golod if and only if the product on Tor^S(R,k) vanishes. Furthermore, we give…

Let $M$ be a cancellative commutative monoid and call a submonoid $S$ of $M$ an undermonoid if $\G(S)=\G(M)$ inside the Grothendieck group of $M$. Gotti and Li asked whether the finite factorization property is hereditary once it is known…

This paper investigates the maximal subgroups of a free projection-generated regular $*$-semigroup $PG(P)$ over a projection algebra $P$, and their relationship to the maximal subgroups of the free idempotent-generated semigroup $IG(E)$…

With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk…

A combinatorial structure, $\mathcal{F}$, with counting sequence $\{a_n\}_{n\ge 0}$ and ordinary generating function $G_\mathcal{F}=\sum_{n\ge0} a_n x^n$, is positive algebraic if $G_\mathcal{F}$ satisfies a polynomial equation…

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.…

For any fixed globally F-regular projective variety X over an algebraically closed field of positive characteristic, we study the F-signature of section rings of X with respect to the ample Cartier divisors on X. In particular, we define an…

An algebra $\A$ is said to be an independence algebra if it is a matroid algebra and every map $\al:X\to A$, defined on a basis $X$ of $\A$, can be extended to an endomorphism of $\A$. These algebras are particularly well behaved…

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…

For a positive real $\alpha$, we can consider the additive submonoid $M$ of the real line that is generated by the nonnegative powers of $\alpha$. When $\alpha$ is transcendental, $M$ is a unique factorization monoid. However, when $\alpha$…

Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G=G_antG_aff, where G_ant is the maximal anti-affine subgroup of G, and G_aff the maximal normal connected affine…

We initiate the study of the expansion $\mathcal{S}(M)$ of a monoid $M$ obtained via the semidirect product of $M$ acting naturally on the left of its power set (regarded as a semilattice under union). We term this the `subset expansion' of…

The free regular $\star$-monoid of rank $r$ is the freest $r$-generated regular monoid $\mathbf{F}_r^\star$ in which every element $m$ has a distinguished pseudo-inverse $m^\star$ satisfying $mm^\star m = m$ and $(m^\star)^\star = m$. We…

Let $(M,\omega_M)$ be a monotone or negatively monotone symplectic manifold, or a Weinstein manifold. One can construct an "action" of $H^1(M,\mathbb{G}_m)$ on the Fukaya category (wrapped Fukaya category in the exact case) that reflects…

In this paper we study some combinatorial aspects of the singular Artin monoids. Firstly, we show that a singular Artin monoid $SA$ can be presented as a semidirect product of a graph monoid with its associated Artin group $A$. Such a…