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
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
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.