Commutative Power-Associative Algebras of Nilindex Four

This is the authors' abstract. We don't add key points for this paper.

The aim of this article is to study the structure of the modules over a trivial algebra of dimension two in the variety ℳ of commutative and power-associative algebras. In particular, we classify the irreducible modules. These results enables us to understand better the structure of finite-dimensional power-associative algebras of nilindex 4.