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The Peirce decomposition for commutative train algebras. (English) Zbl 0810.17025
The author proves the existence of a Peirce decomposition for commutative train algebras of rank $$n$$, satisfying a right rank equation. He gets the relations involving multiplication of the proper subspaces in the Peirce decomposition; then he establishes some consequences of these results for train algebras of rank 4.

##### MSC:
 17D92 Genetic algebras
##### Keywords:
existence; Peirce decomposition; commutative train algebras
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