Related papers: Coproduct Cancellation on \textbf{Act}-$S$

We show that the category of cancellative conjugation semigroups is weakly Mal'tsev and give a characterization of all admissible diagrams there. In the category of cancellative conjugation monoids we describe, for Schreier split…

Let $\mathcal O$ be a holomorphy ring in a global field $K$, and $R$ a classical maximal $\mathcal O$-order in a central simple algebra over $K$. We study sets of lengths of factorizations of cancellative elements of $R$ into atoms…

A monoid $S$ is right coherent if every finitely generated subact of every finitely presented right $S$-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard…

The automorphism groups of certain factorial complex affine threefolds admitting locally trivial actions of the additive group are determined. As a consequence new counterexamples to a generalized cancellation problem are obtained.

In this work, we investigate the commutative monoids over which the axiomatizable class of regular S-acts is primitive normal and antiadditive. We prove that the primitive normality of an axiomatizable class of regular S-acts over the…

An unital C*-algebra A is said to have cancellation of projections if the semigroup D(A) of Murray-von Neumann equivalence classes of projections in matrices over A is cancellative. It has long been known that stable rank one implies…

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…

Walker's cancellation theorem says that if B+Z is isomorphic to C+Z in the category of abelian groups, then B is isomorphic to C. We construct an example in a diagram category of abelian groups where the theorem fails. As a consequence, the…

We prove cancellation theorems for special ideals in Gorenstein local rings. These theorems take the form that if KI is contained in JI, then K is contained in J.

The Zariski cancellation problem plays a central role in affine algebraic geometry and noncommutative algebra, with locally nilpotent derivations providing a fundamental invariant-theoretic approach. This article presents a unified survey…

This article examines the three-way relationship between right coherency of a monoid $S$, solutions of equations over $S$-acts, and injectivity properties of $S$-acts. A monoid $S$ is right coherent if every finitely generated subact of…

Let $H$ be a monoid, $\mathscr F(X)$ be the free monoid on a set $X$, and $\pi_H$ be the unique extension of the identity map on $H$ to a monoid homomorphism $\mathscr F(H) \to H$. Given $A \subseteq H$, an $A$-word $\mathfrak z$ (i.e., an…

We study the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles) in noncommutative rings. To do so, we extend concepts from the commutative theory of non-unique factorizations to a noncommutative setting. Several…

We study the way in which the abstract structure of a small overlap monoid is reflected in, and may be algorithmically deduced from, a small overlap presentation. We show that every C(2) monoid admits an essentially canonical C(2)…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

A set with a group action is referred to as a $G$-set, and the set of functions that commute with this action forms a monoid under function composition. This paper examines the case where the $G$-set is finite, which implies that the monoid…

Absolute integral closures of general commutative unital rings are explored. All rings admit absolute integral closures, but in general they are not unique. Among the reduced rings with finitely many minimal prime ideals, finite products of…

We study properties of a group, abelian group, ring, or monoid $B$ which (a) guarantee that every homomorphism from an infinite direct product $\prod_I A_i$ of objects of the same sort onto $B$ factors through the direct product of finitely…

We prove that if S is a set of functions from a set A to itself, S is closed under composition, and S contains all transpositions of A, then the action of S on Acan be recovered from the semigroup consisting of S together with its…

Extending the work of Bell, Matsuzawa and Satriano, we consider a finite set of polynomials $S$ over a number field $K$ and give a necessary and sufficient condition for the existence of a $N \in \mathbb{N}_{> 0}$ and a finite set $Z…