Related papers: Factorization in Finitely-Presented Monoids
In this paper we study complex representations of the factorpower $\fp(G,M)$ of a finite group $G$ acting on a finite set $M$. This includes the finite monoid $\FP$, which can be seen as a kind of a ``balanced'' generalization of the…
We show that any nonsingular (real or complex) square matrix can be factorized into a product of at most three normal matrices, one of which is unitary, another selfadjoint with eigenvalues in the open right half-plane, and the third one is…
In this paper we give a purely categorical construction of d-fold matrix factorizations of a natural transformation, for any even integer d. This recovers the classical definition of those for regular elements in commutative rings due to…
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the…
A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. Under certain mild conditions on a positive algebraic number $\alpha$, the additive monoid $M_\alpha$ of the evaluation semiring…
The factorisation of the hard amplitude for exclusive meson production in deep inelastic scattering is considered in the framework of a simple model. It is demonstrated explicitly how gauge invariance ensures the cancellation of…
It is well-known that the factorization properties of a domain are reflected in the structure of its group of divisibility. The main theme of this paper is to introduce a topological/graph-theoretic point of view to the current…
Let $M$ be a cancellative and commutative monoid. A non-invertible element of $M$ is called an atom (or irreducible element) if it cannot be factored into two non-invertible elements, while an atom $a$ of $M$ is called strong if $a^n$ has a…
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)…
We study direct-sum decompositions of torsion-free, finitely generated modules over a (commutative) Bass ring $R$ through the factorization theory of the corresponding monoid $T(R)$. Results of Levy-Wiegand and Levy-Odenthal together with a…
Let $D$ be a principal ideal domain and $R(D) = \{\begin{pmatrix} a & b 0 & a \end{pmatrix} \mid a, b \in D\}$ be its self-idealization. It is known that $R(D)$ is a commutative noetherian ring with identity, and hence $R(D)$ is atomic…
In this note, we extend results about unique $n^{\textrm{th}}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified…
Let $\mathcal{S}$ be a small category, and suppose that we are given two (non-full) subcategories $\mathcal{S}^{sm}$ and $\mathcal{S}^{cl}$ that generate all morphisms of $\mathcal{S}$ under composition in the same way as morphisms of…
Factorization structures occur in toric differential and discrete geometry, and can be viewed in multiple ways, e.g., as objects determining substantial classes of explicit toric Sasaki and K\"ahler geometries, as special coordinates on…
The representation theory of finite groups began with Frobenius's factorization of Dedekind's group determinant. In this paper, we consider the case of the semigroup determinant. The semigroup determinant is nonzero if and only if the…
Let $<X>$ be the free monoid on a generating set $X$, and suppose one adjoins to $<X>$ universal 2-sided inverses to a finite set $S$ of its elements. We note an elementary algorithm which yields a normal form for elements of the resulting…
For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by…
We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…
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 initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…