15 citations · 61 across the 13 of their papers we have counts for
15 papers
On atoms and their density in the monoid of monomial ideals
Nikola Bogdanovic, Laura Cossu
We study the structure and distribution of atoms in the monoid of nonzero monomial ideals of the polynomial ring , with . We…
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…
On the finiteness of certain factorization invariants
Laura Cossu, Salvatore Tringali
Let be a monoid, be the free monoid on a set , and be the unique extension of the identity map on to a monoid homomorphism . G…
Factorization under Local Finiteness Conditions
Laura Cossu, Salvatore Tringali
It has been recently observed that fundamental aspects of the classical theory of factorization can be greatly generalized by combining the languages of monoids and preorders. This…
Abstract Factorization Theorems with Applications to Idempotent Factorizations
Laura Cossu, Salvatore Tringali
Let be a preorder on a monoid and be an integer . The -height of an is the sup of the integers for which there is a (strictly)…
Idempotent factorization of matrices over a Prüfer domain of rational functions
Laura Cossu
We consider the smallest subring of containing every element of the form , with . is a Prüfer domain called the minimal Dress…
Idempotent factorizations of singular matrices over quadratic integer rings
Laura Cossu, Paolo Zanardo
Let be the ring of integers of a quadratic number field . We study the factorizations of matrices over into idempotent factors. When $d <…
PRINC domains and comaximal factorization domains
Laura Cossu, Paolo Zanardo
The notion of PRINC domain was introduced by Salce and Zanardo (2014), motivated by the investigation of the products of idempotent matrices with entries in a commutative domain. A…
Minimal Prüfer-Dress rings and products of idempotent matrices
Laura Cossu, Paolo Zanardo
We investigate a special class of Prüfer domains, firstly introduced by Dress in 1965. The {\it minimal Dress ring} , of a field , is the smallest subring of that conta…
Factorizations into idempotent factors of matrices over Prüfer domains
Laura Cossu, Paolo Zanardo
A classical problem, that goes back to the 1960's, is to characterize the integral domains R satisfying the property (IDn): "every singular nxn matrix over R is a product of idempo…