Shorted Operators Relative to a Partial Order in a Regular Ring

TL;DR

This paper derives explicit formulas for maximal elements, called shorted operators, in a subring of a von Neumann regular ring and applies this to electrical circuit theory.

Contribution

It provides a new explicit characterization of shorted operators in regular rings and connects this to electrical circuit applications.

Findings

Explicit form of maximal shorted operators derived

Application to electrical circuit shorted operators

Unique shorted operator identified in the context of circuits

Abstract

In this paper, the explicit form of maximal elements, known as shorted operators, in a subring of a von Neumann regular ring has been obtained. As an application of the main theorem, the unique shorted operator (of electrical circuits) which was introduced by Anderson-Trapp has been derived.