Rings used in modal logic and their radicals (Q1862716)

In this paper the authors prove that each modal Boolean ring without identity can be embedded in a modal Boolean ring with identity. The method they use for the proof is a common one in the case of rings. Moreover, they develop a radical theory for modal Boolean rings for modal logics such as T and S4. They also give a characterization theorem for the semisimple classes of modal Boolean rings.