6 papers
Categorical Algebra of Atomic Monoids: Presentability, Regularity, and Pretorsion Theories
Federico Campanini, Laura Cossu
We study the category of atomic monoids and atom-preserving homomorphisms. We prove that is locally finitely presentable by exhibiting a strong…
On the arithmetic of polynomial ideals
Nikola Bogdanovic, Laura Cossu, Azeem Khadam
This paper investigates atomic factorizations in the monoid of nonzero ideals of a multivariate polynomial ring , under ideal multiplication. Building on recent…
On the arithmetic of power monoids
Laura Cossu, Salvatore Tringali
Given a monoid (written multiplicatively), the family of all non-empty finite subsets of containing the identity element is itself a…
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties
Federico Campanini, Laura Cossu, Salvatore Tringali
We introduce and investigate the category of atomic monoids and atom-preserving monoid homomorphisms, which is a (non-full) subcategory of the usual category of m…
Realization of spaces of commutative rings
Laura Cossu, Bruce Olberding
Motivated by recent work on the use of topological methods to study collections of rings between an integral domain and its quotient field, we examine spaces of subrings of a commu…
Some applications of a new approach to factorization
Laura Cossu
As highlighted in a series of recent papers by Tringali and the author, fundamental aspects of the classical theory of factorization can be significantly generalized by blending th…