Abstract Let $f:\mathbb {C}^2\to \mathbb {C}^2$ be a polynomial skew product that leaves invariant an attracting vertical line $ L $. Assume moreover $f$ restricted to $L$ is non-uniformly hyperbolic, in the sense satisfies one of following conditions: (1) $f|_L$ topological Collet–Eckmann and weak regularity conditions. (2) The Lyapunov exponent at every critical value point lying Julia set $f...

We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4) are constr...

In this paper, we study skew cyclic and skew constacyclic codes over the ring R = Fq + uFq + vFq + uvFq where q = p^m; p is an odd prime, u^2 = u; v^2 = v; uv = vu. We show that Gray image of a skew cyclic code of length n is a skew quasi-cyclic code of length 4n over Fq of index 4. We also study the structural properties of skew cyclic and skew constacyclic codes over R. Further, generating po...

The first aim of this note is to fill a gap in the literature by giving proof following refinement Shafarevich's theorem on solvable Galois groups: Given global field $k$, finite set $\mathcal{S}$ primes and group $G$, there extension $k$ $G$ which all are totally split. To that end, we prove that, given every split embedding problem $G \rightarrow {\rm{Gal}}(L/k)$ over with nilpotent kernel ha...

This paper is concerned with ideals in a commutative Noetherian ring R of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of R generated by regular sequences exhibit a desirable type of ‘uniform’ behaviour. The principal technical tool used is a result, proved by R. Hartshorne and R. Speiser in the case where R is local and contains its residue fi...