Dr. Gordon Swain was on study leave during the
spring 2019 semester. During that time, he has been working on answering the
following problem, ““Suppose the equation f 1 (x)yg 1 (z)+ f 1 (x)zg 2 (y)+ f 2
(y)xg 1 (z)+ f 2 (y)zg 3 (x)+ f 3 (z)xg 2 (y)+ f 3 (z)yg 3 (x)=0 for all elements x,y,z in a
given prime ring. What does this imply about the functions f i and g j and about the prime
ring itself?” The aim is to show that if the functions are non-trivial, then they have a
‘linear’ form, and the ring is very similar to a matrix ring.
While researching, he stayed in Ashland. He did
come to his office from time to time and still completed duties within the
department.
