Ω-Algebras with split products

We introduce Ω-sp-algebras as a generalization of dialgebras to the case of Ω-algebras. Given a variety of algebras (Formula presented.), we provide a criterion for an Ω-sp-algebra to be a (Formula presented.) -sp-algebra. We give examples of Ω-sp-algebras such as associative sp-systems, ternary Filippov sp-algebras, Lie triple sp-systems, and Bol sp-algebras. We prove a lifting theorem for the term functor and the triviality of every simple Ω-sp-algebra.