International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 209-214

Universally catenarian domains of D+M type, II

David E. Dobbs1 and Marco Fontana2

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 T be a domain of the form K+M, where K is a field and M is a maximal ideal of T. Let D be a subring of K such that R=D+M is universally catenarian. Then D is universally catenarian and K is algebraic over k, the quotient field of D. If [K:k]<, then T is universally catenarian. Consequently, T is universally catenarian if R 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.