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
additional algebraic domain assume called coefficients column class commutative Consider corollary corresponding critical minor D and E D₁ D₁₂ defined determined diagonal block diagonal element divisor domain elements in F elements in Ra enlarged matrices equal example exists a unimodular factors field finding form H further G₂ hand hence Hermite form implies independent indicated integral irreducible basis k-by-k blocks k-by-k matrices last column left associates Lemma linear combination MacDuffee main diagonal matrices with elements matrix H method minimal basis multiplication necessary and sufficient non-singular Note operation particular possible principal ideal ring problem proof rank rational reduced regarded relation represents respect rows rows and columns serves shown Steinitz studying sufficient condition Suppose Theorem theory thesis transformations unimodular matrix unique unit written X₁₂ zero