Left-associated Matrices with Elements in an Algebraic Domain |
Contents
Algebraic Domains | 13 |
Enlarged Matrices | 18 |
Necessary Conditions | 25 |
3 other sections not shown
Common terms and phrases
a₂ adjugate algebraic domain algebraic integers algebraic number class number coefficients column class column from right common ideal divisor common right divisor commutative condition that matrices critical minor D₁₂ d₂ defined diagonal block diagonal element domain F elements in Ra elements of H enlarged matrices exist matrices exists a matrix exists a unimodular factors field form H G₂ greatest common divisor greatest common right H₂ hence ideal a,,a implies irreducible basis irreducible polynomial k-by-k blocks k-by-k matrices kn-by-kn left associates left-associated matrices Lemma 13 Lemma 9 linear combination MacDuffee main diagonal Math matric representative matrices with elements matrix H minimal basis minor determinants modulo the diagonal necessary and sufficient non-principal class non-principal ideal non-singular non-zero rows polynomial principal ideal ring principal or non-principal r+1 rows reduced relation rows and columns Steinitz sufficient condition takes D₁ Theorem unimodular matrix X₁₂ zero rows