Extension of the multiplication operation in E-algebras to an A-morphism of E-algebras and Cartan objects in the category of May algebras.

It is proved in the paper that the multiplication operation on an arbitrary E-algebra can be extended to an E-algebra A-morphism. As a corollary, it is proved that every May algebra defined by an E-algebra is a Cartan object in the category of May algebras. [ABSTRACT FROM AUTHOR]