Train algebras of rank 3 with finiteness conditions
A train algebra of rank \(r\) is a commutative baric algebra \((A,\omega)\) satisfying the so-called train equation of \(A\): \[ x^r+\gamma_1\omega(x)x^{r-1}+\cdots+\gamma_{r1}\omega(x)^{r-1}x=0. \] This paper deals with train algebras of rank 3. In particular, it is proved that any Noetherian (or Artinian or finitely generated) train algebra of rank 3 is finitely dimensional.
scientific article; zbMATH DE number 5574588
scientific article