Rigid, quasi-rigid and matrix rings with (σ,0)-multiplication - Abdioglu, C.; Şahinkaya, S.; KÖR, A. (Algebra and Discrete Mathematics, 2014)
Let R be a ring with an endomorphism σ. We introduce (σ, 0)-multiplication which is a generalization of the simple 0- multiplication. It is proved that for arbitrary positive integers m ≤ n and n ≥ 2, R[x; σ] is a reduced ring if and only if Sn,m(R) is a ring with (σ, 0)-multiplication.