Power-associative algebras that are train algebras
The authors investigate the structure of power-associative algebras which also are train algebras. In particular: -- The train equation of such an algebra is determined. -- In the finite-dimensional case, it is shown that the dimensions of the Peirce components are invariant and that the upper bounds for their nil-indexes are reached for some idempotent. -- It is shown that locally train algebras are, in fact, train algebras. Moreover, the set of idempotents is studied in detail and special attention is paid to the Jordan and Bernstein cases.
scientific article; zbMATH DE number 5833414
scientific article