ABSTRACT
For a ring with (nonzero) zero divisors, questions involving integrality properties often have answers which deal more with the relationship between the ring and its ring of finite fractions rather than with that between the ring and its total quotient ring. This chapter begins with the formal development of the ring of finite fractions. It presents a theorem that can not only characterizes when the ring is completely integrally closed but also completely describes the complete integral closure when it is not.
