International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 209-214
Universally catenarian domains of type, II
1Department of Mathematics, University of Tennessee, Knoxville 37996-1300, TN, USA
2Dipartimento di Matematica, Universita di Roma, “La Sapienza”, Roma 00185, Italy
Received 26 January 1990
Copyright © 1991 David E. Dobbs and Marco Fontana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a domain of the form , where is a field and is a maximal ideal
of . Let be a subring of such that is universally catenarian. Then is
universally catenarian and is algebraic over , the quotient field of . If , then is
universally catenarian. Consequently, is universally catenarian if is either Noetherian or a
going-down domain. A key tool establishes that universally going-between holds for any domain
which is module-finite over a universally catenarian domain.