On Jordan ideals and matrix rings

For A, a commutative ring, and A=M2(A), results by Costa and Keller characterize certain Ep(2,A)-normalized subgroups of the symplectic group, Sp(2,A) via structures utilizing Jordan ideals and the notion of radices. The following work creates a Jordan ideal structure theorem for Z2-graded rings, A0⊕A1, and a Z2-graded matrix algebra. The major theorem is a generalization of Costa and Keller’s previous work on matrix algebras over commutative rings.