Duplicate of a train algebra and of a periodic Bernstein algebra (Q1906777)

The author shows that if \(A^2\) is a train algebra of rank \(r\), then the duplicate of \(A\) is train of rank \(r + 1\). Also, if \(A^2\) is a Bernstein algebra of order \(n\) and period \(p\), the commutative duplicate of \(A\) is Bernstein of order \(n + 1\) and period \(p\).