Ideals of some Green biset functors

Abstract: In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of M C-group, this definition generalizes that of a B-group, given for the Burnside functor. Given a Green biset functor A, with the above hypotheses, the set of all M C-groups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the M C-groups of A.