“Factorization Spaces”
Mercoledì 22 Giugno 2022, ore 16:30 - Aula 2BC30 - Laura Cossu (Karl-Franzens-Universität, Graz)
Abstract
Combining the language of monoids and preorders, we introduce the notion of “factorization space” (“F-space” for short) as a unifying framework to study factorizations of certain elements of a monoid H through the elements of a subset A of H. F-spaces allow to make sense of concepts like “factoriality”, “bounded factorization”, “elasticity” etc., in settings (such as rings with non-trivial zero divisors) where the classical definitions, introduced for atomic factorizations over commutative and/or unit-cancellative monoids, would make little sense in practice. For certain classes of F-spaces we also show some arithmetical results that extend analogous classical ones.
The talk is based on joint work with S. Tringali.
