A characterization of Sheffer functions by hyperidentities (Q1101139)

A Sheffer function is a function f: A \(n\to A\) such that the algebra \b{A}\(=<A;f>\) is primal. A hyperidentity for a universal algebra \b{A} is an identity for its clone of operations. The paper gives a new primality criterion, i.e. a characterization of Sheffer functions in terms of hyperidentities: If \(| A|\) is a prime power, then f: A \(n\to A\) is a Sheffer function iff the algebra \b{A}\(=<A;f>\) satisfies neither of two given unary hyperidentities. The cases \(| A| \in \{2,3,4\}\) are treated as examples.