International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 209-214
doi:10.1155/S0161171291000212
Universally catenarian domains of D+M 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.
Abstract
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.