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math.RA2025
Dual coalgebras of twisted tensor products
Manuel L. Reyes
We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is a…
math.RA2025
A tour of noncommutative spectral theories
Manuel Reyes
This is a survey of noncommutative generalizations of the spectrum of a ring, written for the Notices of the American Mathematical Society.
math.RA2024
The domain and prime properties for Koszul rings and algebras
Manuel L. Reyes, Daniel Rogalski
We establish a technique to prove that a Koszul graded ring is prime or a domain using information about its Koszul dual. This is based on a general categorical result that expands…