A large class of MDS linear codes is constructed. These are endowed with an efficient decoding algorithm. Both the definition and design their algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, first part paper develops a direct presentation by means parity-check matrices, rests upon matrix maps manipulations. The somewhat more sophisticated mat...

Describing the subgroup structure of a non-commutative division ring is subject an intensive study in theory rings particular, and skew linear groups general. This still so far to be complete. In present paper, we this problem for weakly locally finite rings. Such constitute large class which strictly contains

A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if (I ∩ J) = (I) + (J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f (x) = a0 + a1x + ··· + amx, g(x) = b0 + b1x + ··· + bnx ∈ R[x] satisfy f (x)g(x) = 0, then aibj = 0 for each ...

In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.

We extend the notion of finite embedding problems over fields, a central in inverse Galois theory, to situation centrally division rings. first show that solving problem such ring H is equivalent finding solution some center involving polynomial constraint. then every constant split skew field rational fractions H(t) with indeterminate t has solution, if an ample field, thus providing non-commu...