Bacterial Division: The Fellowship of The Ring

Right sided heart evaluation after successful mitral valve replacement.

Introduction: It is well-documented that right-sided heart dysfunction and significant tricuspid valve regurgitation (TVR) have adverse effects on patient outcomes after left-sided heart valve surgery. Therefore, the evaluation of right ventriclular (RV) function and TR severity in patients who had undergone mitral valve replacement (MVR), associated with/without concomitant su...

Triangularization over finite-dimensional division rings using the reduced trace

In this paper we study triangularization of collections of matrices whose entries come from a finite-dimensional division ring. First, we give a generalization of Guralnick's theorem to the case of finite-dimensional division rings and then we show that in this case the reduced trace function is a suitable alternative for trace function by presenting two triangularization results. The first one...

Triangulaizability of Algebras Over Division Rings

On nest modules of matrices over division rings

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.