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 are domains such that is an LFD universally going-down domain and is algebraic over , then the inclusion map satisfies GB for each . However, for any nonzero ring and indeterminate over , the inclusion map is not universally (S)GB.
@article{AMBP_2003__10_2_245_0, author = {David E. Dobbs and Gabriel Picavet}, title = {On {Strong} {Going-Between,} {Going-Down,} {And} {Their} {Universalizations,} {II}}, journal = {Annales math\'ematiques Blaise Pascal}, pages = {245--260}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {10}, number = {2}, year = {2003}, doi = {10.5802/ambp.175}, mrnumber = {2031270}, zbl = {1071.13003}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.175/} }
TY - JOUR AU - David E. Dobbs AU - Gabriel Picavet TI - On Strong Going-Between, Going-Down, And Their Universalizations, II JO - Annales mathématiques Blaise Pascal PY - 2003 SP - 245 EP - 260 VL - 10 IS - 2 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.175/ DO - 10.5802/ambp.175 LA - en ID - AMBP_2003__10_2_245_0 ER -
%0 Journal Article %A David E. Dobbs %A Gabriel Picavet %T On Strong Going-Between, Going-Down, And Their Universalizations, II %J Annales mathématiques Blaise Pascal %D 2003 %P 245-260 %V 10 %N 2 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.175/ %R 10.5802/ambp.175 %G en %F AMBP_2003__10_2_245_0
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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