Power-associative algebras that are train algebras (Q615812)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Power-associative algebras that are train algebras |
scientific article; zbMATH DE number 5833414
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Power-associative algebras that are train algebras |
scientific article; zbMATH DE number 5833414 |
Statements
Power-associative algebras that are train algebras (English)
0 references
7 January 2011
0 references
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.
0 references
absolutely primitive idempotent
0 references
Bernstein algebra
0 references
Jordan algebra
0 references
Peirce decomposition
0 references
principal idempotent
0 references
power-associative algebra
0 references
stable algebra
0 references
train algebra
0 references
0 references
