On Strong Going-Between, Going-Down, And Their Universalizations, II
Annales mathématiques Blaise Pascal, Volume 10 (2003) no. 2, pp. 245-260.

We consider analogies between the logically independent properties of strong going-between (SGB) and going-down (GD), as well as analogies between the universalizations of these properties. Transfer results are obtained for the (universally) SGB property relative to pullbacks and Nagata ring constructions. It is shown that if AB are domains such that A is an LFD universally going-down domain and B is algebraic over A, then the inclusion map A[X 1 ,,X n ]B[X 1 ,,X n ] satisfies GB for each n0. However, for any nonzero ring A and indeterminate X over A, the inclusion map AA[X] is not universally (S)GB.

DOI: 10.5802/ambp.175
David E. Dobbs 1; Gabriel Picavet 2

1 University of Tennessee Department of Mathematics Knoxville, Tennessee 37996-1300 U.S.A.
2 Université Blaise Pascal Laboratoire de Mathématiques Pures 63177 Aubière Cedex FRANCE
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David E. Dobbs; Gabriel Picavet. On Strong Going-Between, Going-Down, And Their Universalizations, II. Annales mathématiques Blaise Pascal, Volume 10 (2003) no. 2, pp. 245-260. doi : 10.5802/ambp.175. https://ambp.centre-mersenne.org/articles/10.5802/ambp.175/

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