5 papers
The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale
Matthew Bolan, Joachim Breitner, Jose Brox +31
We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project suc…
An elementary algebraic proof of the fundamental theorem of algebra
Katelyn S. Clark, Pace P. Nielsen
We provide a new, elementary, algebraic proof of the fundamental theorem of algebra. Furthermore, the method recovers a more general version of the theorem recently obtained by Jos…
Euclidean domains with no multiplicative norms
Caleb J. Dastrup, Pace P. Nielsen
We construct a Euclidean domain with no multiplicative Euclidean norm to a compatibly well-ordered monoid, and hence with no multiplicative Euclidean norm to (under it…
Levels of cancellation for monoids and modules
Pere Ara, Ken Goodearl, Pace P. Nielsen +3
Levels of cancellativity in commutative monoids , determined by stable rank values in for elements of , are investigated. The behavior of t…
The separativity problem in terms of varieties and diagonal reduction
Pere Ara, Ken Goodearl, Pace P. Nielsen +2
We provide two new formulations of the separativity problem. First, it is known that separativity (and strong separativity) in von Neumann regular (and exchange) rings is tightly c…