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On perspective Abelian groups

Grigore Calugareanu, Andrey Chekhlov

Abstract

As a special case of perspective R-modules, an Abelian goup is called perspective if isomorphic summands have a common complement. In this paper we describe many classes of such groups.

On perspective Abelian groups

Abstract

As a special case of perspective R-modules, an Abelian goup is called perspective if isomorphic summands have a common complement. In this paper we describe many classes of such groups.
Paper Structure (7 sections, 29 theorems)

This paper contains 7 sections, 29 theorems.

Table of Contents

  1. Introduction
  2. Generalities on perspective modules
  3. Perspective Abelian groups
  4. Definition
  5. Reduction theorems
  6. Perspective $p$-groups
  7. Perspective torsion-free groups

Key Result

Theorem 2.1

For a module $M_{S}$ with $R=\mathrm{End}_{S}(M)$, the following conditions are equivalent: (1) $M$ is perspective. (4) If $erse=e$ for some $e^{2}=e,r,s\in R$, then $erte=e$ for some $t\in R$ such that $ete\in U(eRe)$. In particular, $M_{S}$ is perspective iff $R_{R}$ is perspective, i.e., perspect

Theorems & Definitions (54)

  • Theorem 2.1
  • Corollary 2.2
  • proof
  • Proposition 2.3
  • Corollary 2.4
  • Remark 2.5
  • Theorem 2.6
  • Proposition 3.1
  • Proposition 3.2
  • proof
  • ...and 44 more