Biring Theory and Its Galois Theory of Rings

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.

Key Words:

• Algebra
• Algop
• Bialgebroid
• Bimodule
• Biring
• Central simple
• Coring
• Galois descent
• Galois theory
• Preservation
• Ring

2010 Mathematics Subject Classification:

• Primary 16D10, 16D20
• Secondary 16W20, 16W30

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.