Year: 2013
Type: preprint
Abstract: Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated localizations of D and projections onto partially ordered quotient groups of G(D). We use this functor to construct many cochain complexes of o-homomorphisms of po-groups. These complexes naturally lead to some fundamental structure theorems and some natural homology theory that provide insight into the factorization behavior of D.
Source: arXiv (Cornell University)
Authors: Coykendall, Jim, Goodell, Brandon
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1673523503