Direct Division in Factor Rings

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 ...

Constructing Division Rings as Module-theoretic Direct Limits

If R is an associative ring, one of several known equivalent types of data determining the structure of an arbitrary division ring D generated by a homomorphic image of R is a rule putting on all free R-modules of finite rank matroid structures (closure operators satisfying the exchange axiom) subject to certain functoriality conditions. This note gives a new description of how D may be constru...

The Possible Involvement of Nitric Oxide/Endothelium Derived Relaxing Factor in Atropine-Induced Vasorelaxation

Atropine has been used to block cholinergic neurotransmission in basic research. Large doses of atropine cause vasodilation of the blood vessels in the skin. This effect is apparently unconnected with the antimuscarinic activity of atropine and seems to be due to a direct action on the blood vessels. It has been suggested that atropine blocks muscarinic receptors at low doses and it induces th...