In this paper we study plenary train algebras of arbitrary rank. We show that for most parameter choices of the train identity, the additional identity (x2 − ω(x)x)2 = 0 is satisfied. We also find sufficient conditions ...

The existence of idempotent elements in plenary train algebras of rank greater than 3, is an open problem to be solved. J. Carlos Gutierrez's results on plenary train algebras in Gutierrez (2000) are based on the underlying ...