December 3, 2024

I am happy to announce my newest paper. We characterize fixed product preserving mappings on Cayley-Dickson algebras of characteristic not 2 (a multiplication table for a CD algebra is shown to the left). There's some surprises in there. Jordan homomorphisms of octonion algebras are not easily describable in terms of automorphisms and anti-automorphisms. Fixed product preserving maps therefore have interesting forms, but zero product preserving maps (for split CD algebras) are essentially ring homomorphisms. It also turns out that finite-dimensional alternative algebras are zero product determined. Nice.

I am happy to announce the publication of my newest paper. It is on maps preserving inverses on alternative division rings. The paper is largely a test case for maps satisfying some kind of weak inverse identity: f(x)f(y)f(x) = f(x) whenever xyx = x, where the latter defines the weak inverse. In particular, the relationship to Jordan automorphisms and there's some interesting phenomena for characteristic 2. 

I am delighted to announce that I am joining the Math, Applied Math, and Statistics faculty at Case Western Reserve University, starting Fall 2024, as an Instructor of Mathematics. 

Thank you to my previous institution, Niagara University, for investing in me. I regret not being able to stay longer. Best wishes to everyone past, present, and future at Niagara University!