A note on subgroups in a division ring that are left algebraic over a division subring

Algebraic Division Ring Extensions1

A Note on the Multiplicative Group of a Division Ring

Let K be a noncommutative division ring with center Z and multiplicative group K*. Hua [2; 3] proved that (i) K*/Z* is a group without center, and (ii) K* is not solvable. A generalization (Theorem 1) will be given here which contains as a special case (Theorem 2) the fact that K*/Z* has no Abelian normal subgroups. This latter theorem obviously contains both (i) and (ii). As a further corollar...

A Novel Noise Reduction Method Based on Subspace Division

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

A Note on a graph associated to a commutative ring

The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$.  In Section 2 of this articl...

A Novel Noise Reduction Method Based on Subspace Division

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...