The Birkhoff-von Neumann Theorem has been proved many times in the literature with a number of different methods, some inductive, some constructive, some existential. We offer a new proof that is a little more direct than most, though nonconstructive.

If (A,B) is a reachable linear system over commutative von Neumann regular ring R, finite collection of idempotent elements defined, constituting complete set invariants for the feedback equivalence. This allows us to construct explicitly canonical form. Relations are given among this idempotents and various other families invariants. For systems fixed sizes, equivalent classes put into 1-1 cor...

We study the first order theory of Bezout difference rings. In particular we show that rings of sequences very rarely have decidable theories as difference rings, or even decidable model completions. MSC: 03C60, 03B25, 12H10, 13L05