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Unit-regularity and representability for semiartinian *-regular rings

Christian Herrmann

Abstract

We show that any semiartinian subdirectly irreducible *-regular ring R admits a representation within some inner product space.

Unit-regularity and representability for semiartinian *-regular rings

Abstract

We show that any semiartinian subdirectly irreducible *-regular ring R admits a representation within some inner product space.

Paper Structure

This paper contains 6 sections, 5 theorems.

Table of Contents

  1. Erratum
  2. Introduction
  3. Preliminaries: Regular and $*$-regular rings
  4. Preliminaries: Representations
  5. Main results
  6. Examples

Key Result

Theorem 1

A semiartinian regular ring is unit-regular provided all its homomorphic images are directly finite.

Theorems & Definitions (9)

  • Theorem 1
  • Theorem 6
  • proof
  • Theorem 7
  • proof
  • Proposition 8
  • Lemma 9
  • proof
  • proof