MINIMAL NONCOMMUTATIVE REVERSIBLE AND REFLEXIVE RINGS

Reflexive–EP elements in rings

We define and characterize reflexive–EP elements in rings, that is elements which commute with their image-kernel (p, q)-inverse.

Orderings for Noncommutative Rings

Introduction and Notation. The goal of this paper is to present the beginnings of a theory of real algebraic geometry for noncommutative rings. For a basic introduction to the commutative theory, see Lam [L]. The word field will be used in this paper to mean a (generally noncommutative) skewfield; we shall specify a commutative field when we need to. R will denote a noncommutative ring with 1. ...

Extensions of strongly alpha-reversible rings

We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...

Reversible Rings with Involutions and Some Minimalities

In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, ∗-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of ∗-reversible rings. It is proved here that the polynomial rings of ∗-reversible rings may...

Noncommutative Extensions of Hilbert Rings