T-LINKED EXTENSIONS, THE T-CLASS GROUP, AND NAGATA THEOREM

Let A be a subring of the integral domain B. Then B is said to be t-li nked over A if for each finitely generated ideal I of A with I-1 = A, we have (IB)-1 = B. If A and B are Krull domains, this condition is eq uivalent to PDE. We show that if B is t-linked over A, then the map I- ->(IB)t gives a homomorphism from the group of t-invertible t-ideals o f A to the group of t-invertible t-ideals of B and hence a homomorphis m Cl(t)(A)-->Cl(t)(B) of the t-class groups. Conditions are given for these maps to be surjective which extend Nagata's Theorem for Krull do mains to a much larger class of domains including, e.g., Noetherian do mains each of whose grade-one prime ideals has height one.