Elementary Divisor Theorem for Noncommutative Pids
Copyright policy )Elementary Divisor Theorem for Noncommutative Pids
We prove that, over a PID, if two matrices A {\mathbf {A}} and B {\mathbf {B}} have the same size, present isomorphic modules and have rank ≥ 2 \geq 2 , then A {\mathbf {A}} is equivalent to B {\mathbf {B}} . This answers a question raised by Nakayama in 1938. Our solution makes use of a number of facts about the algebraic K K -theory of noetherian rings.
- University of Wisconsin System United States
- University of Southern California United States
- University of Wisconsin–Oshkosh United States
- University of California System United States
- National Academy of Sciences United States
Algebraic systems of matrices, Canonical forms, reductions, classification, elementary divisor theorem, modules over principal ideal domains, Divisibility, noncommutative UFDs, Representation theory of associative rings and algebras, Endomorphism rings; matrix rings, Vector and tensor algebra, theory of invariants, invertible matrices, cancellation
Algebraic systems of matrices, Canonical forms, reductions, classification, elementary divisor theorem, modules over principal ideal domains, Divisibility, noncommutative UFDs, Representation theory of associative rings and algebras, Endomorphism rings; matrix rings, Vector and tensor algebra, theory of invariants, invertible matrices, cancellation
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