In this work, linearized multivariate skew polynomials over division rings are introduced. Such right linear the corresponding centralizer and generalize polynomial finite fields, group or differential rings. Their natural evaluation is connected to remainder-based of free polynomials. It shown that P-independent sets those given by linearly independent when partitioned into conjugacy classes. ...

Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized — the Smith form, and its skew-symmetric variant obtained via unimodular congruences. Applications include the analysis of the eigenvalue and elementary divisor structure of products of two skew-symmetric matrices, the derivation of a Smith-McMillan-like canonical form for skew-symmetric rational m...

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

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.

Let R be a ring, α an automorphism, and δ an α-derivation of R. If the classical quotient ring Q of R exists, then R is weak α-skew Armendariz if and only if Q is weak α-skew Armendariz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly ci...