BiHom-pre-alternative algebras and BiHom-alternative quadri-algebras

The purpose of this paper is to introduce and study the notion of BiHom-pre-alternative algebra which may be viewed as a BiHom-alternative algebra whose product can be decomposed into two compatible pieces. Furthermore, we introduce the notion of BiHom-alternative quadri-algebra and show the connections between all these algebraic structures using Rota-Baxter operators and O-operators.