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

Citation

Bull. Amer. Math. Soc. 55 (1949), 117-118

Abstract

We prove the following theorem: 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.