On \(\ast\)-clean group rings over finite fields (Q2031658)

A ring is clean if each of its elements is the sum of a unit and an idempotent. A \(*\)-ring is \(*\)-clean if each of its elements is the sum of a unit and a projection (a self-adjoint idempotent). If \(G\) is a finite abelian group and \(F\) a finite field, the authors explore \(*\)-cleanness of the group ring \(FG.\) In particular, they consider two types of involutions on \(FG\) and characterize when \(FG\) is \(*\)-clean in terms of these involutions. For the classical involution on \(FG\), they also characterize \(*\)-cleanness of \(FG\) in terms of some properties of the LCD abelian codes.