On Matrices with Elements in a Principal Ideal Ring

Authors

William Leavitt, University of Nebraska - Lincoln
George Whaples, Indiana University

Date of this Version

1949

Comments

Published in Bull. Amer. Math. Soc. 55 (1949) 117-118. Used by permission.

Abstract

We prove the following theorem.
THEOREM 1. Let D be any commutative principal ideal ring without divisors of zero, and A any matrix with elements in D whose characteristic equation factors into linear factors in D. Then there exists a unimodular matrix T, with elements in D, such that T^-1 AT has zeros below the main diagonal.