In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v, uv = vu, q = p and p is an odd prime. We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.

We study the Smith forms of matrices form f ( C g ) where t , ∈ R [ ] is an elementary divisor domain and companion matrix (monic) polynomial . Prominent examples such are circulant matrices, skew-circulant triangular Toeplitz matrices. In particular, we reduce calculation to that F G quotients by some common divisor. This allows us express last non-zero determinantal as a resultant. A key tool...

In this paper, using generalized partial skew versions of Armendariz rings, we study the transfer of left (right) zip property between a ring R and partial skew generalized power series rings