The Classification Problem of Finite Rings by Computable Means.

Abstract

This thesis establishes a constructive method for testing when two given finite rings are isomorphic. Currently published theory has classified a significant number of finite rings; however, idealized representatives are almost always used, with no provision for determining which isomorphism class an arbitrary ring belongs. The new results are as follows: 1) Two rings are isomorphic if and only if a specific system of quadratic equations is satisfied. 2) As a corollary, there exists a system of linear equations that positively identify whether or not a ring R possesses a 1. The system also shows how to change a ring's basis so that 1 becomes a basis element. Some tests for existence of other idempotents besides 1 are shown. 3) Some old and new results in classifying finite rings of small rank are obtained.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA185869

Entities

People

  • William A. Kiele

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Algorithms
  • Asymetric Encryption
  • Classification
  • Computations
  • Computer Programs
  • Computers
  • Coordinate Systems
  • Cryptography
  • Differential Equations
  • Equations
  • Notation
  • Quadratic Equations
  • Security
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Graph Algorithms and Convex Optimization.