Accession Number : ADA185869
Title : The Classification Problem of Finite Rings by Computable Means.
Descriptive Note : Doctoral thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
Personal Author(s) : Kiele, William A
PDF Url : ADA185869
Report Date : Jan 1987
Pagination or Media Count : 140
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.
Descriptors : *RINGS(MATHEMATICS), CLASSIFICATION, LINEAR ALGEBRAIC EQUATIONS, QUADRATIC EQUATIONS, COMPUTATIONS, THESES, COMPUTER PROGRAMS
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE