Abstract
Biring theory is about birings (A, P), that is, algops (A, P) of an associative algebra A and (A, A)-biring P acting on A via a morphism γ: P → Pres F A from P to the terminal (A, A)-biring Pres F A of preservations of A. (The word biring is used in a theory for a structure with unit, product, counit, coproduct subject to conditions of the theory.) Biring theory has its central simple theory and its Galois theory of rings. Its Galois birings are the reduced simple birings.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENTS
This paper has benefited greatly from the wise and helpful observations and suggestions of the referees. It is a pleasure to thank them at this time.
Notes
Communicated by L. Small.