Let f(x) = ∑d s=0 asx s ∈ Z[x] be a polynomial with ad 6≡ 0 mod p. Take z ∈ Fp and let Oz = {fi(z)}i∈Z+ ⊂ Fp be the orbit of z under f , where fi(z) = f(fi−1(z)) and f0(z) = z. For M < |Oz|, we study the diameter of the partial orbit Oz,M = {z, f(z), f2(z), . . . , fM−1(z)} and prove that diam Oz,M & min { M c log logM , Mp , M 1 2p 1 2 } , where ‘diameter’ is naturally defined in Fp and c depe...

We provide an algebraic description for sum-rank metric codes, as quotient space of a skew polynomial ring. This approach generalizes at the same time group algebra setting rank-metric codes and in Hamming metric. allows to construct twisted linearized Reed-Solomon new family maximum distance extending Sheekey's Gabidulin rank Furthermore, we analogue Trombetti-Zhou construction, which also pro...

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

We survey three methods for proving that the characteristic polynomial of a finite ranked lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on Zaslavsky’s theory of signed graphs. The second approach is algebraic and employs results of Saito and Terao about free hyperplane arrangements. Finally we con...