An e-ring is a pair (R,E) consisting of an associative ring R with unity 1 together with a subset E ⊆ R of elements, called effects, with properties suggested by the so-called effect operators on a Hilbert space. We establish the basic properties of e-rings, investigate commutative e-rings called c-rings, relate certain c-rings called b-rings to Boolean algebras, and prove a structure theorem f...

we give a survey of recent applications of group rings to combinatorics and tocryptography, including their use in the di erential cryptanalysis of block ciphers.