3 papers
math.AC2024
A Universal Property of the Spectrum of a Ring and the Semiring of its Ideals
William Bernardoni
Arithmetic valuations are intimately connected with the structure of the ideals of a commutative ring. We show how the generalized idempotent semiring valuations of Jeffrey and Noa…
math.RA2023
Applications of Generalized Universal Valuations
William Bernardoni
We introduce a generalization of the universal valuation semiring defined by Jeffrey and Noah Giansiracusa. We then explicitly characterize the additive structure of this semiring…
math.AT2023
Algebraic and Geometric Models for Space Networking
William Bernardoni, Robert Cardona, Jacob Cleveland +6
In this paper we introduce some new algebraic and geometric perspectives on networked space communications. Our main contribution is a novel definition of a time-varying graph (TVG…