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arXiv · 1302.4759

A Homological Approach to Factorization

Jim Coykendall·Brandon Goodell
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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.

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Jim Coykendall, Brandon Goodell. 2013-02-19. A Homological Approach to Factorization. https://arxiv.org/abs/1302.4759

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