ON UNIQUE FACTORIZATION MODULES

On Unique Factorization Semilattices

The class of unique factorization semilattices (UFSs) contains important examples of semilattices such as free semilattices and the semilattices of idempotents of free inverse monoids. Their structural properties allow an efficient study, among other things, of their principal ideals. A general construction of UFSs from arbitrary posets is presented and some categorical properties are derived. ...

Lectures On Unique Factorization Domains

On the Factorization of Differential Modules

Differential modules are modules over rings of linear (partial) differential operators which are finite-dimensional vector spaces. We present a generalization of the Beke-Schlesinger algorithm that factors differential modules. The method requires solving only one set of associated equations for each degree d of a potential factor. Mathematics Subject Classification (2000). 13N05; 13N10; 13N15;...

Foundations and Unique Factorization

This is a difficult question to answer: number theory is an area, or collection of areas, of pure mathematics that have been studied for well over two thousand years. As such, it means different things to different number theorists (of which I am one). Nevertheless the question is not nearly as subjective as “What is truth?” or “What is beauty?”: all of the things that various people call numbe...

Shuue Factorization Is Unique

We prove that, given a nite set of words S, there exists at most one (normalized) multiset P such that S is the shuue of the words in P. The multiset P is eeectively computable.