We give necessary and sufficient conditions for a skew polynomial ring K[t; σ, δ] over a division ring K to be a left V -domain. In particular, when this ring admits a unique simple left module, the conditions obtained include: 1) all polynomials are Wedderburn, 2) all n× n matrices over K are (σ, δ)-similar. We also provide necessary and sufficient conditions for this ring to be both left and ...

Linear codes may be endowed with cyclic structures by means of skew polynomial rings. This is the case of Piret cyclic convolutional codes [26] and the subsequent generalizations and alternatives (see [27], [14], [11], [25], [16], [20]). Non commutative cyclic structures of this kind have been also considered for block linear codes ([7], [5], [4], [12], [1]), and for linear codes over commutati...

This paper introduces skew dihedral group rings and their applications for public-key cryptography. We present a specific ring that is the underlying algebraic platform our cryptographic constructions. then build two-party key exchange protocol an analysis of its security. exploit it to derive agreement protocol, probabilistic scheme, encapsulation mechanism. In addition security constructions,...

two digraphs of same order are said to be skew-equienergetic if theirskew energies are equal. one of the open problems proposed by li andlian was to construct non-cospectral skew-equienergetic digraphs onn vertices. recently this problem was solved by ramane et al. inthis paper, we give some new methods to construct new skew-equienergeticdigraphs.

A Leavitt labelled path algebra over a commutative unital ring is associated with space, generalizing algebras graphs and ultragraphs as well torsion-free generated by idempotents. We show that can be realized partial skew group rings, Steinberg algebras, Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, description of diagonal preserving isomorphisms cha...

Let K be a field of characteristic p > 0. It is proved that the group Autord(D(Ln)) of order preserving automorphisms of the ring D(Ln) of differential operators on a Laurent polynomial algebra Ln := K[x ±1 1 , . . . , x n ] is isomorphic to a skew direct product of groups Z n p⋊AutK(Ln) where Zp is the ring of p-adic integers. Moreover, the group Autord(D(Ln)) is found explicitly. Similarly, A...

This article continues investigation of ways to obtain pseudo-random sequences over Galois field via generating LRS over Galois ring and complication it. Previous work is available at http://eprint.iacr.org/2016/212 In this work we provide low rank estimations for sequences generated by two different designs based on coordinate sequences of linear recurrent sequences (LRS) of maximal period (MP...