On Duo Rings

Quasi-Duo Rings and Stable Range Descent

In a recent paper, the first author introduced a general theory of corner rings in noncommutative rings that generalized the classical theory of Peirce decompositions. This theory is applied here to the study of the stable range of rings upon descent to corner rings. A ring is called quasi-duo if every maximal 1-sided ideal is 2-sided. Various new characterizations are obtained for such rings. ...

Deadly duo

An astonishing one-third of the world’s population is infected with the bacterium that causes tuberculosis (TB), Mycobacterium tuberculosis. In most people it remains inactive or latent but in about 10% of people an active case of TB disease will develop within their lifetime. Simple antibiotics can prevent and treat most of these cases, yet 8-10 million people develop an active TB infection an...

2 5 O ct 2 00 4 ORE EXTENSIONS OVER DUO RINGS

We show that there exist noncommutative Ore extensions in which every right ideal is two-sided. This answers a problem posed by Marks in [5]. We also provide an easy construction of one sided duo rings.

The solo/duo gap

*-σ-biderivations on *-rings

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...