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 ...

Train algebras were introduced by Etherington in 1939 as an algebraic framework for treating genetic problems. The aim of this paper is to study the representations and irreducible representations of power-associative ...

A presente pesquisa, vinculada à linha “Processos Formativos, Ensino e Aprendizagem”, foi implusionada pela questão: Qual a relação entre a álgebra acadêmica e a álgebra escolar expressa nas concepções dos licenciandos e ...

We give a characterization of the representations on train algebras of rank 3. We prove that the subalgebra of the algebra of endomorphisms of a module generated by the representation of the nil ideal of the algebra is ...

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 ...