Date of this Version
Bull. Amer. Math. Soc. 55 (1949), 117-118
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.